Is it possible for the probability of an event to be relative, i. e. valued differently for different objective observers? Does this say anything pertinent about the feasibility of unifying quantum mechanics and relativity?
Just doing the calculations informally in my head, it seems to me, that for two inertial observers, of a same quantum phenomenon, the probability distribution is modified just so that an event happens at (x,t) in S with probability P, then it happens in at (x',t') in S' with the same probability, where (x',t') is related to (x,t) by a Lorentz transformation.
But what I don't understand is why you posted the question in the math forum. It is not the task of math to say what is and what is not physically possible. A mathematician just has to say "Let P1 be the probability of the event according to S and let P' be the probability of the event according to S'" and it's done.