I am sure you know this one already, but ...
The director announces that next week will be a fire drill. In order to make it more realistic the day of the drill will be a surprise.
Here is the problem: The drill cannot be on Friday (the last day of the work week), because everybody would know on Friday morning that if the drill did not happen yet it will have to be this day, so it would not be a surprise.
But for the same reason it cannot be on Thursday, because everybody knows it cannot be on Friday and on Thursday morning, knowing that it did not happen yet one would have to conclude it will be this day, so it would not be a surprise. etc.
Therefore the fire drill cannot be on any day.
But on Tuesday the alarm bell rings and of course nobody knew it would be that day...
C.F. v. Weizsäcker discussed the puzzle in his book 'Aufbau der Physik', assuming that it tells us something about the nature of time.
According to Wikipedia no consensus on its correct resolution has yet been established despite significant academic interest (*).
Maybe we should try to assign Bayesian probabilities. Obviously, we have p(Fri) = 0 but then it follows that ...
(*) Notice the citation of the famous remark made by Defense Secretary Donald Rumsfeld!