"Any type of event that has nonzero probability will happen infnitely many times(...). This undermines the basis for probabilistic predictions of local experime

"Any type of event that has nonzero probability will happen infnitely many times(...). This undermines the basis for probabilistic predictions of local experiments. If infnitely many observers throughout the universe win the lottery, on what grounds can one still claim that winning the lottery is unlikely? To be sure, there are also infnitely many observers who do not win, but in what sense are there more of them?" The first sentence is wrong, as pointed out by zeteo, but the rest does not make any sense either. Take continuous random walk starting at zero at t=0. There are an infinite number of paths that reach each value at time t=1. Yet we can say the the probability that the random walk is positive at t=1 is one half. And by "say" I mean give a solid mathematical definition of this fact, not some hand waving argument.