**A**lthough I have already discussed this point repeatedly on this ‘Og, I found myself replying to [yet] another question on X validated about the apparent paradox of conditioning on a set of measure zero, as for instance when computing

**P**(X=.5 | |X|=.5)

which actually has nothing to do with Bayesian inference or Bayes’ Theorem, but is simply wondering about the definition of conditional probability distributions. The OP was correct in stating that

**P**(X=x | |X|=x)

was defined up to a set of measure zero. And even that

**P**(X=.5 | |X|=.5)

could be defined arbitrarily, prior to the observation of |X|. But once |X| is observed, say to take the value 0.5, there is a zero probability that this value belongs to the set of measure zero where one defined

**P**(X=x | |X|=x)

arbitrarily. A point that always proves delicate to explain in class…!