The probability of both, in that case, plummets, and you should start looking at other explanations. Like, say, that the victim was shot with a rifle at close range, which only leaves a bullet in the body 1% of the time (or whatever).

It might be true that, between two hypotheses one is now more likely to be true than the other, but the probability for both still dropped, and your confidence in your pet hypothesis should still drop right along with its probability of being correct.

So say you have hypothesis X at 60% confidence and hypotheses Y at 40% New evidence comes along that shifts your confidence of X down to 20%, and Y down to 35%. Y didn't just "win". Y is now even more likely to be wrong than it was before the new evidence came it. The only substantive difference is that now X is probably wrong too. If you notice, there's 45% probability there we haven't accounted for. If this is all bound up in a single hypothesis Z, then Z is the one that is the most likely to be correct.

Contradictory evidence shouldn't make you more confident in your hypothesis.