&gt; If the null-hypothesis is true, every observation made should be consistent with it. This will result in P(X|H) trending to 1<p>Every observation being consistent with H <i>doesn&#x27;t</i> mean that for each event X that occurs, the conditional probability of X given H will be, or &quot;trend toward&quot;, 1.  Assuming a perfectly deterministic universe, the P(X|everything else that is true) will be 1 for every X that occurs, but that doesn&#x27;t mean P(X|H) for any particular true proposition H will be anything like that.