To use Bayes to update here, you must determine the conditional probabilities as they were before you knew that M occurred, and could thus update to P(M)=1. If one did not already know that M happened then one certainly could not say `P(M|R) = P(M|~R) = 1`. One might be able to claim `P(M|R) = P(M|~R) = P(M)`, which is just saying the events are independent.
Certainly with a prior that the events are independent, then you won't be able to update your probability of R by knowing that M did happen, any more than knowing last nights lotto numbers would probability of R.
In reality, things are even worse, as assuming independence is not fully reasonable, so you will end up with uncertainly about how or if the variables relate. One could assume some form of meta probability distribution of various ways the variables could relate, but then direct application of Bayes formula not feasible. You would still in that scenario not be learning much if anything useful about P(R).
Certainly with a prior that the events are independent, then you won't be able to update your probability of R by knowing that M did happen, any more than knowing last nights lotto numbers would probability of R.
In reality, things are even worse, as assuming independence is not fully reasonable, so you will end up with uncertainly about how or if the variables relate. One could assume some form of meta probability distribution of various ways the variables could relate, but then direct application of Bayes formula not feasible. You would still in that scenario not be learning much if anything useful about P(R).