In this article applied and theoretical epistemologies benefit each other in a study of the British legal case of R. vs. Clark. Clark's first infant died at 11 weeks of age, in December 1996. About a year later, Clark had a second child. After that child died at eight weeks of age, Clark was tried for murdering both infants. Statisticians and philosophers have disputed how to apply Bayesian analyses to this case, and thereby arrived at different judgments about it. By dwelling on this applied case, I make theoretical gains: clarifying and defending pragmatic principles of inference that are important for estimating key probabilities in a range of cases. Then, partly by drawing on such principles, and uncovering overlooked data on post‐partum psychosis, I make applied gains: improving the rationality of judgments about the Sally Clark case in particular, judgments important to future similar cases.