I have two questions which I found answers to slightly different version of them in books but not to those that I have in mind so please pay attention in responding.

1) I like to calculate the expectation of conditional probability Pr(X|Y) for all values of Y. Meaning I want to integrate Pr(X|Y) over all positive Y. What is the formula for that? I found the answer to expectation of Pr(X|Y) for all values of X.

[you can consider any arbitrary probability function]

2) How can I calculate the probability of Pr(X|YZ)? Where Z and Y are two different dependent events. I found the answer to Pr(XY|Z).

Thank you