 When \(H\) entails \(E\), the theory says the evidence must be true, so the discovery of the evidence fits the theory perfectly. Our formalism vindicates the truism in this special case as follows. When \(H\) entails \(E\), Conditional Certainty for Logical Consequences tells us that \(p(E\mid H)=1\), so Bayes’ theorem becomes:  \[p(H\mid E) = p(H)\frac{1}{p(E)}\]