Bayesian conditioning and logical public announcements track each other at a semantic level, meaning their outputs amount to the same thing.

If the new information is of the hard type, accepted as irrevocably true by all agents, the probabilistic counterpart of logical public announcements is Bayesian conditioning. Both notions track each other at a semantic level, meaning that their outputs amount to the same thing. Computing beliefs after a public announcement means recomputing in the submodel consisting of all states where the information received was true. This is exactly the same mechanism as for recalculating probabilities in B