I think the 0.5 probability is correct, if we're talking about frequency of particular experiences. (Of course, that's not always what we're talking about, as in the Sleeping Beauty non-paradox, but in a situation like this, where there's no decision contingent on your probability estimate and you immediately know the outcome, presumably you mainly just want to know how much any given experience should surprise you.) If we assume that the duplication process is instantaneous and non-destructive, then, at the moment the duplication takes place, you know that there will soon be twice as many agents with a mind-state identical to yours, and that 50% of them will subjectively experience what feels like suddenly teleporting (to wherever the duplicator is constructing the copy).