First of all, I think you are conflating prior and posterior probabilities. P(brown skin | illegal) != P(illegal | brown skin). The standard for a police stop

First of all, I think you are conflating prior and posterior probabilities. P(brown skin | illegal) != P(illegal | brown skin). The standard for a police stop is reasonable suspicion. Do you think having brown skin in Arizona is reasonably suspicious? But much more importantly, the statistical evidence (which you haven't shown) would only be a consideration if justice were a statistical property. But if justice were a statistical property, there should be no objection to giving police arbitrary discretion to make stops and searches, since statistically speaking it is overwhelmingly likely that a citizen chosen at random has committed some illegal act for which they have not yet been convicted. But somehow that reasoning does not seem as appealing when we are the ones staring down the barrel of it.