 Bayesian confirmation

Evidence $E$ confirms $H$ relative to background $K$ when it increases its conditional probability. With $0<P(H\mid K)<1$ and positive evidence probability, Bayes' theorem givesIndeed, writing $p=P(H\mid K)$, $a=P(E\mid H,K)$ and $b=P(E\mid \neg H,K)$ gives the posterior probability $pa/(pa+(1-p)b)$; comparison with $p$ reduces to $a>b$. Thus scientific confirmation depends on the alternatives and background, not just on a statement's logical form.