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The probability that an event A will occur, when another event B is known to occur or to have occurred. It is commonly denoted by P(A|B).

From stat.yale.edu:

"The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This probability is written P(B|A), notation for the probability of B given A. In the case where events A and B are independent (where event A has no effect on the probability of event B), the conditional probability of event B given event A is simply the probability of event B, that is P(B). If events A and B are not independent, then the probability of the intersection of A and B (the probability that both events occur) is defined by P(A and B) = P(A)P(B|A)."

Excerpt reference: Wikipedia.