A photo containing faces of two different people is compared to labeled images of faces in database. The probability of a match on the first person is .70. The probability of a match on the second comes back as .90.
If the faces were totally independent (ie two unrelated photos), one would expect the probability of a joint match to be .7*.9 or .63 and one would expect the probability of neither matching to be .30*.10 or .03. The remainder would be attributable to one matching and the other not.
However, the faces may not be totally independent insofar as they appear in the same photo of people interacting with one another.
Question: Should one treat these matches as wholly independent? If not, how would one update the probability of one given the probability of the other, and what would be their joint probability? I can imagine using Bayes Law but not sure if that is the right tool.