In probability theory, **conditional probability** is the probability that some event *A* occurs, knowing that event *B* occurs.
It is written *P*(*A*|*B*), read "the probability of *A*, given *B*".

If *A* and *B* are events, and *P*(*B*) > 0, then

*P*(*A*|*B*) =*P*(*A*∩*B*) /*P*(*B*).

*A*and

*B*are independent events (that is, the occurrence of either one does not affect the occurrence of the other in any way), then

*P*(

*A*∩

*B*) =

*P*(

*A*) ·

*P*(

*B*), so

*P*(

*A*|

*B*) =

*P*(

*A*).

If *B* is an event and *P*(*B*) > 0, then the function *Q* defined by *Q*(*A*) = *P*(*A*|*B*) for all events *A* is a probability measure.

Conditional probability is more easily calculated with an decision tree.