i.e. the sum of the relative entropy of p ( a ) the prior distribution for a from the updated distribution u ( a ) , plus the expected value (using the probability distribution u ( a ) ) of the relative entropy of the prior conditional distribution p ( x ∣ ∣ a ) from the new conditional distribution q ( x ∣ ∣ a ) . (Note that often the later expected value is called the conditional relative entropy (or conditional Kullback–Leibler divergence) and denoted by D KL ( q ( x ∣ ∣ a ) ∥ ∥ p ( x ∣ ∣ a ) ) ) This is minimized if q ( x ∣ ∣ a ) = p ( x ∣ ∣ a ) over the whole support of u ( a ) ; and we note that this result incorporates Bayes' theorem, if the new distribution u ( a ) is in fact a δ function representing certainty that a has one particular value.