It won't change "fundamentally" i.e. in any important way, but it will slightly change the meaning of the probability decreasing on average, because for example, the probability of all hypotheses of complexity 17 might be 0, and if this is the case then there is no greater complexity which will give a lower probability for this particular value. But in any case either the terms will sum to 1 after a finite number of values, in which case the probability will drop permanently to 0 after that, or it will not, in which case the theorem will continue to hold as applied to all the hypotheses that have some positive probability.

Just because there are infinitely many options doesn't mean that it's reasonable to assign a probability of 1/infinity. These options are claims about reality that you make with a language; saying that their probability is such a value is much the same as if I said that the probability that you are right in this disagreement is 1/infinity. If someone can say this in the context of my argument, he can say it any context, and this would not be standard probability theory.