probability priority of comma and bar In probability does , have priority over |?
I am asking because of below question.
Is below X and (Y given by Z)?
P(X,Y|Z)
or is it (X and Y) given by Z?

To answer your question more directly, yes, comma (,) has higher priority than bar (|) when interpreting this notation.
So P(X,Y|Z) is the conditional probability of X and Y occurring together, given Z. It might help to think of this case as P((X,Y)|Z) (though such use of additional brackets is not common in the notation, afaik).
Similarly, P(X|Y,Z) is the conditional probability of X, given Y and Z (i.e. as if there were additional brackets as follows: P(X|(Y,Z)).
