I get what you mean, but I think you've formulated this incorrectly. Let P(Y) be your prior about government corruption. Let X be the event that SBF is arrested. You want to compute P(Y|X) using the Bayesian update formula and then set P(Y) = P(Y|X). That is what is meant by re-evaluating your priors.

You're modelling X and Y as propositions and you're correct about the inference of ~X and ~Y, but Bayesian updating is about degree of belief in those propositions, which your inference is not a claim about.