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The denominator $P(B)$ ensures that the posterior probability $P(A \mid B)$ sums to 1 over all possible mutually exclusive events $A$. It scales the product of the likelihood and prior to a valid probability distribution.

Conditions: Bayes' theorem is written in probability form: $P(A \mid B) = \frac{P(B \mid A)P(A)}{P(B)}$.

The denominator $P(B)$ ensures that the posterior probability $P(A \mid B)$ sums to 1 over all possible mutually exclusive events $A$. It scales the product of the likelihood and prior to a valid probability distribution.

Conditions: Bayes' theorem is written in probability form: $P(A \mid B) = \frac{P(B \mid A)P(A)}{P(B)}$.