We have introduced probability as a language for expressing our degrees of belief or uncertainties about events. Whenever we observe new evidence (i.e., obtain data), we acquire information that may affect our uncertainties. A new observation that is consistent with an existing belief could make us more sure of that belief, while a surprising observation could throw that belief into question. Conditional probability is the concept that addresses this fundamental question: how should we update our beliefs in light of the evidence we observe?
2.1 The importance of thinking conditionally
Conditional probability is essential for scientific, medical, and legal reasoning, since it shows how to incorporate evidence ...