Conditional Probability

Conditional probability is the probability of one event given that another event is already known to have happened, written P(A given B). Knowing the extra information shrinks your world to only the cases where B is true, and you ask how often A also holds there.

It is the engine behind learning from data: every time new evidence updates your belief, you are computing a conditional probability. A classic trap is confusing P(A given B) with P(B given A); the probability that someone has a disease given a positive test is usually very different from the probability of a positive test given the disease.