Or, to put it in macroscopic terms, just before Dumbledore read the parchment, how should an observer estimate the probability that the message will be "No" rather than "Don't count on it".

There's been work specifically on this question about expectations for simplified cases when one has a 2D Newtonian system with wormholes violating causality. Kip Thorne discusses this in some of his books although I don't remember if the results are due to him or to someone else. The upshot is that at least in limited circumstances, one can make meaningful statements.