Harry was wondering if he could even get a Bayesian calculation out of this. Of course, the point of a subjective Bayesian calculation wasn’t that, after you made up a bunch of numbers, multiplying them out would give you an exactly right answer. The real point was that the process of making up numbers would force you to tally all the relevant facts and weigh all the relative probabilities. Like realizing, as soon as you actually thought about the probability of the Dark Mark not-fading if You-Know-Who was dead, that the probability wasn’t low enough for the observation to count as strong evidence. One version of the process was to tally hypotheses and list out evidence, make up all the numbers, do the calculation, and then throw out the final answer and go with your brain’s gut feeling after you’d forced it to really weigh everything. The trouble was that the items of evidence weren’t conditionally independent, and there were multiple interacting background facts of interest...

Relevant excerpt from Chapter 86 of HPMOR: