Assume that I evaluate the probability that a murder suspect is guilty to 10%. Then I find a blood trace at the scene and only 1% of the population has this blood type. The suspect has this blood type and the test is accurate (say 100% accuracy for simplicity). What is now the probability that the suspect is guilty?
posterior = prior x likelihood / normalization = .1 x 1 / .01 = 10
What am I missing here?