In the Richard III case, the hypothesis being evaluated was that the Leicester skeleton was Richard III. The prior probability was not zero — the researchers had chosen to excavate a specific location based on historical evidence pointing to that location — but it was not high either. Buckley’s estimate of nine to one against finding the grave within the site provides a rough starting point: even with good historical evidence for the friary location, finding the actual grave was not considered likely.
Each piece of evidence then updated this prior in favor of or against the identification. The male sex was consistent with Richard III, but not informative enough to substantially distinguish him from the many other men buried in medieval friaries. The approximate age at death was consistent, and somewhat more informative because it added another constraint. The scoliosis was highly informative because it was a distinctive physical characteristic that a contemporary had noted in Richard specifically. The battle injuries were consistent and suggestive without being definitive. The radiocarbon dating was consistent and narrowed the field. The mitochondrial DNA match was highly informative because the haplogroup and specific sequence were rare and matched two independently identified living descendants.
The 6.7 million to one figure represents the output of the Bayesian model after incorporating all of these updates simultaneously. It is not the result of any single test. It is not the accuracy of a DNA test kit. It is the answer to the question: given all the evidence available, what are the odds that this skeleton is Richard III rather than some other individual who happened to share all of these characteristics?