Editing Probability space (section)

=== Conditional probability ===
{{Main article|Conditional probability}}
Kolmogorov's definition of probability spaces gives rise to the natural concept of conditional probability.  Every set {{mvar|A}} with non-zero probability (that is, {{math|''P''(''A'') > 0}}) defines another probability measure
<math display="block"> P(B \mid A) = {P(B \cap A) \over P(A)} </math>
on the space. This is usually pronounced as the "probability of ''B'' given ''A''".

For any event {{math|''A''}} such that {{math|''P''(''A'') > 0}}, the function {{math|''Q''}} defined by {{math|1=''Q''(''B'') = ''P''(''B''&nbsp;{{!}}&nbsp;''A'')}} for all events {{mvar|B}} is itself a probability measure.