 The theorem is equally commonsensical for cases where no crucial experiment is available. To see what it says in such cases, consider an example. Let \(h_i\) be some theory that implies a specific rate of proton decay, but a rate so low that there is only a very small probability that any particular proton will decay in a given year. Consider an alternative theory \(h_j\) that implies that protons never decay. If \(h_i\) is true, then for a persistent enough sequence of observations (i.e., if proper detectors can keep trillions of protons under observation for long enough), eventually a proton decay will almost surely be detected. When this happens, the likelihood ratio becomes 0. Thus, the posterior probability of \(h_j\) becomes 0.