Interesting thing about probability theory: presupposed is identity of each claimed re-occurrence as an instance of the same thing or kind.  Insofar as an identity gap exists intervening each instance of identity, and each instance is different from every other instance if it is to be a different instance of occurrence, which probability theory requires, then some autonomous criterion of identity is requisite.  Requisite here is memory, when memory cannot be verified insofar as it cannot be re-experienced.  Putting the issue of memory aside, however, since different instances cannot be the same if they are to be different instances, then they need be identified by analogy.  Insofar as each instance presumably has infinite properties, then analogy requires an a priori finite identity of "relevant" properties.  Necessarily arbitrary insofar as elemental properties are infinite, then there is no objective necessity to probability.  Neither can a rule resolve this difficulty.  Insofar as the properties of an object are infinite, they cannot be encompassed by a rule, for the rule need be limitless.  Analogy with an immediately available archetype is possible, but the problem of identity reoccurs insofar as different individuals can focus on different properties of archetype and autotype.  Matters worsen considering identity according to a rule or archetype are both constituent of consciousness, and consciousness is privileged, so the conscious identity of another is unknowable.  But, let us put this latter aside as well, and return to the issue of identity in itself.  Simply enough, because of the problem of infinity, an a priori rule of identity is impossible.  Identity is possible only a posteriori by individual subjective judgments.  Thus, whether a particular probability calculation is correct or not is empirically relative to the observer.  It is necessary only insofar as assumed a priori, independently of empirical observation.  Of course, a divergent observer can be dismissed a priori, but this is necessarily ad hominem, logically fallacious as such.  Illustrated, however, is how the very nature of probability rests upon nominal definition, when as exhibited by some commenters here, it is presumed to rest upon "reality".  Here "reality" is an odd notion indeed, insofar as it is assumed independent of human consciousness, yet only knowable by observation, when observation is a state of human consciousness.  Unable to be experienced in itself, like other unexperienced suppositions, it need be categorized as imaginary, when imagination is dismissed as "unreal". Confusion abounds.