 What about when the theory fits the evidence less than perfectly? If we think of fit as the certainty with which \(H\) predicts \(E\), \(p(E\mid H)\), then the previous analysis generalizes nicely. Suppose \(H\) predicts \(E\) strongly, but not with absolute certainty: \(p(E\mid H) = 1 - \varepsilon\), for some small number \(\varepsilon\). Applying Bayes’ theorem again, we have:  \[ p(H\mid E) = p(H)\frac{1-\varepsilon}{p(E)}\]