You have probation period for a reason. Maybe you even like the job. Don't think too hard about it. Corporates are not your personal friends. "Bad Rep" means nothing (look at CEOs who drive companies into walls and just get picked up by the next one).
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hmm, I don't think I'm aware of any probation periods in any official sense, never had one before on previous contracts, though those have typically been freelance rather than employed. What differentiates this period from normal employment? Shorter notice periods on each side? How long does it usually last?
It’s not reasonable that it would give you a bad reputation, but real talk: in a small town and a small industry it might. If you tell them that you’ve got the commitment, they might work with you to allow a leave period, but they’re not super likely to. If this is the industry you had been working in, maybe you can check with a previous mentor?
Edit: if you are going to tell them, wait until you have an offer.
If you haven't been offered a position yet, then just be honest with them that you have a commitment coming up that you made before the offer. Let them decide if they still want to hire you. Who knows, they may agree to the time off.