Rational evidence for a given theory is the observation of an event that is more likely to occur if the theory is true than if it is false. (The event would be rational evidence against the theory if it is less likely if the theory is true.)
The likelihood ratio term $\frac{P(B | A)}{P(B|\neg A)}$ from Bayes' theorem is greater than 1 if the event B is evidence of the theory A, and less than 1 if the event is evidence against the theory.