This would then go down to theoretical physics and whether or not it was already defined which box you would choose. I think something closer to the Schrödinger's cat experiment, and whether the cat will die. In this case, I think you could objectively say the probability is 50/50.
The wave function collapses as you induce probabilistic action. And once again, to speak of probability one must speak temporally. Lack of observation of the change does not negate the change in probability.
