One of the common ways to use conditional probability is through Bayes' Theorem. The definition of conditional probability is used in Bayes' Theorem to render inferences in many situations where events are causally linked.
Generalizations
Bayes theorem for 3 events
A version of Bayes' theorem for 3 events results from the addition of a third event , with , on which all probabilities are conditioned:
Derivation
Using the chain rule
And, on the other hand
The desired result is obtained by identifying both expressions and solving for .