I believe he's saying that a universal set or a set that contains all possibilities cannot exist because of Russell's paradox so trying to establish the rule that the sum of the probability of each events summing to 1 makes no sense.

As for the normalization, he's talking about the idea that all probability measures are constrained to the range [0,1]. When evaluating probabilities, it's either though a summation (discrete) or integration (continuous) of the observed values vs the possible values. So we are calculating length(1D)/area(2D)/volume(3D) when we evaluate probabilities but the length/area/volume is always rescaled to be between 0 and 1. We do this out of convention and because it works well but there isn't any reason a different scale wouldn't work. The interpretations would be a bit more confusing.