[kuboble]

I think the trickiest part is that the other party willingly shared some information and their motives affect probabilities way more than any math.

I find it easier to think about this problem stated like this: let's say you go around asking people " do you have exactly 2 children and at least one of them is a boy?". What are the odds of them having 2 boys if they answered yes.

[HWR_14]

All probability questions suffer from the same bias. The Monty Hall problem doesn't work if the person offering the choice has some agency and motives.