What does this notation mean p(x|y)?

Question

I was reading through a paper, when I encounter p(a|s). What does this mean? It was in context with log probability but I cant find this notation anywhere.

Answer 1

That is standard notation for conditional probability.

See here for example for further information.

Answer 2

Like everyone else said, it's just notation for conditional probability. Here is the textbook that I used last semester in my probability class. Flip to page 141 and you can read all about the conditional probability, both in discrete and continuous cases.

Answer 3

The notation P(x|y) means P(x) given event y has occurred, this notation is used in conditional probability.

There are two cases if x and y are dependent or if x and y are independent.

Case 1) P(x|y) = P(x&y)/P(y)

Case 2) P(x|y) = P(x)