 If increasing evidence drives towards 0 the likelihood ratios comparing each competitor \(h_j\) with hypothesis \(h_i\), then the odds against \(h_i\), \(\Omega_{\alpha}[{\nsim}h_i \pmid b\cdot c^{n}\cdot e^{n}]\), will approach 0 (provided that priors of catch-all terms, if needed, approach 0 as well, as new alternative hypotheses are made explicit and peeled off). And, as \(\Omega_{\alpha}[{\nsim}h_i \pmid b\cdot c^{n}\cdot e^{n}]\) approaches 0, the posterior probability of \(h_i\) goes to 1. This derives from the fact that the odds against \(h_i\) is related to and its posterior probability by the following formula: