Otdfbt

I'd say, you should not try to disclose any information you're not supposed to know, in first place.

In this case, however, you can do some good with the knowledge, question is "how".

You mentioned,

I happened to overheard a conversation between him and a manager, and he is apparently suffering from the Alien hand syndrome.

So that manager has the knowledge of the problem and can explain / handle the situation better. What you should do, is to point the new employee to talk to that manager. Drop a subtle hint, that should do. Something like

"Hm, that's weird, I never heard any complaints like that when I worked here. However, I believe you can talk to X (that manager), he might know better as I believe they had worked together for quite sometime."

This way, you're indirectly vouching for that person (which would at least have a positive impression) for the time you worked there and pointing the new employee to someone who can actually help to resolve the confusion.

There is a middle-ground option, though I'll leave it to your judgment if you think it's too close to just revealing the truth:

You can mention that disorders which would cause that behavior exist, without suggesting that you know someone has such a disorder.

In my observation people often react primarily to things being out of the ordinary, and not with a rational examination of why those unusual things might happen. This new worker would probably accept that medical conditions exist and might explain odd behavior, but instead is thinking in the other direction to suggest that the odd behavior simply indicates an odd person.

I think that your "I never paid much attention" response is great. You could naturally follow it up with something like

I wonder what might cause something like that. I've read that there are some medical conditions which might do it. I don't know, but I doubt [coworker X] would be touching himself in the office, that really doesn't sound like him.

This approach lets you acknowledge her experience without joining in and validating her view of the coworker as weird, while subtly hinting that a legitimate explanation for the behavior might exist.

This might be too close to revealing the truth for your preferences, but since you don't "officially" know I think it would be understood more as a possibility than you transmitting secret, definitely-true information. Often people just need to be reminded that disorders which cause unusual behaviors exist in order to back off a bit.

If that was the case should I disclose the illness to prevent misunderstandings ? or is it really completely unethical, and none of my business ?

No, yes, maybe (see below) - in that order.

Should you ever find yourself in a similar position in the future the best thing to do is to privately bring it to the attention of the person with the illness. That way they can decide whether they would rather clear up any misunderstanding by disclosing their condition or choose to let it go and keep the condition private.

It's totally not OK to disclose someone's medical conditions to third parties without their consent, unless seeking or obtaining the person's consent is impractical and there's an actual emergency that sort of thing.

It doesn't really matter if you have privileged information or not. My answer would be the same in either case. I would say something like:

There are all sorts of reasons why someone's hands might be moving strangely. When I don't know the full context, I try to give people the benefit of the doubt.

This gently gives them a little guilt about gossiping, provides guidance for how to proceed, and doesn't even disclose that you know anything confidential, let alone hint at what that confidential information might be.

Yeah, it's a tough one but you did leave in a get-out-of-jail-free card in your question: the person with the syndrome told his manager.

Tell her that if it really bothers her she should talk to her manager about the guy's behaviour. Management are aware of his condition and they should, if they are decent human beings (tall order, I know), be able to handle it in a delicate manner.

This is one of those circumstances where it is reasonable to pass the buck.

If you answer the question of this new employee in a professional manner you should use only this knowledge you are allowed to share. Some accidentially overheared talks are not included to this.

You say the ill employee is a former colleague of yours. So you would have experience with him. If you feel the need to defend him you can tell the new employee about his character, behavior and so on during the time you have worked together. Give examples showing the "strange but not dangerous" behavior of this hand...

If you want to give the new employee a advice "how to act professional if you are not there" you can send her to the manager. (That this may solve the information deficit of her is a nice side effect.)

(With a lot of "Fingerspitzengefühl" (LEO says: sure instinct/tact/intuition/flair) you could make a joke about some movie character with the same illness, but this is in almost all cases not suitable.)

If your old colleague wanted his co-workers to know about his condition, then he would tell them. Since he hasn't told them, he doesn't want them to know, so you should respect that and not say anything about his illness.

To the person you talked to, you might say something like "I know my ex-colleague very well. Because I know him so well, I can assure you one hundred percent that he was not touching himself. That's all I can say".

I do not have the reputation to add this as comment to @Sourav Ghosh's answer, so adding as an answer.

New employee - N

Former Colleague - F

Manager - M

As mentioned in the question, since M knows about it and to avoid any awkwardness for F who is already suffering from the illness, I say, instead of telling N to talk to M, inform M, if it is a viable option, to talk to N or find any other way to have this situation addressed so that F does not have to go through this again.

That way, since this information is coming from the higher up, it has more value and s/he would know that the condition F is experiencing, has been acknowledged at the organization and not something you are making up to protect F.

Also, since you do not work there, you do not have to worry about thinking of this as going behind N's back. You're just trying to save the awkwardness for everyone and adding credibility about F's condition by having it addressed from the management.

I think it is possible to address this without divulging anything too personal. When faced with the situation you describe, you could have responded:

"Oh, I believe he has a medical condition but I don't know the details. Maybe you could speak to them about it or ask their manager."

Saying that you don't know the details might be a white lie, but it would head off any follow-up questions they might be tempted to ask.

I have experienced this before many years ago, when I had made an unfortunate joke about a colleague, and someone told me they had a medical problem which obviously caused me some embarrassment, but meant I didn't question it any further and was more understanding about their behaviour.