&gt;Every observation being consistent with H doesn&#x27;t mean that for each event X that occurs, the conditional probability of X given H will be, or &quot;trend toward&quot;, 1.<p>Agreed. If you plot P(X|H) (computed over all observations) over time, in a well-formed experiment the line will trend to 1 if the null-hypothesis is true and to 0 if the null-hypothesis is false.<p>It really is that simple.