This standard notation for $~$\\mathbb P(X \\mid Y)$~$ meaning "the probability of $~$X$~$, assuming $~$Y$~$ to be true" is a helpfully symmetrical vertical line, to avoid giving you any visual clue to remember that the assumption is on the right and the inferred proposition is on the left\.

This confused me at first because I didn't realize it was sarcasm and I thought I was missing something. "Is there any reason why distinguishing between assumption and proposition is a bad idea?"