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DuncanS comments on two puzzles on rationality of defeat - Less Wrong
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As a point of detail, if P1, P2 and P3 imply T, then R,P1,P2 and P3 can only imply ~T if the system R,P1,P2,P3 is inconsistent. To fix this in your argument, simply have R replace one of the other axioms rather than supplement it.
Other than that, I can only recommend what others have said about Bayes theorem - it is the correct weapon with which to approach problems of this type.