Indeed, a prior conviction raises the Bayesian probability of a given suspect having committed a similar crime. In probability terms, the prior probability of s

Indeed, a prior conviction raises the Bayesian probability of a given suspect having committed a similar crime. In probability terms, the prior probability of suspect S having committed crime Cn, given that they committed crime C0, C1, etc., is certainly higher than without that information. But how much higher? Given 8 billion people in the world, the priors are quite low for any given person P having committed any particular crime Cn. On the other hand, humans (including jurors) are liable to bias, and without other alternatives they can very easily be fooled. By the time someone has been dragged in front of you, and you're told that they committed C0, C1, etc., then you're asked if they committed crime C and to you it looks very plausible because it's hard to take into account the (still) very low prior, especially if you lack other alternative hypotheses. So while you're right that it is a valid inference, we choose not to allow that inference in order to counter the much higher magnitude of bias caused by the representativeness heuristic and the like.