My solution is this: In point 2. the solution starts talking about probabilities without defining the sample space. And this is why the solution is nonsensica

My solution is this: In point 2. the solution starts talking about probabilities without defining the sample space. And this is why the solution is nonsensical. "One envelope contains twice as much as the other" does not define a sample space, so it is too early to start talking about probabilities. If you say "the sample space is all pairs of natural numbers where one is twice as big as the other", then what are the probabilities assigned to each pair? They cannot be pairwise equal because the space is infinite. So even if probabilities for (X, 2*X) and (X, X/2) happen to be equal for a particular X, they definitely cannot be equal for every X, so the "infinite swap" doesn't hold anymore.