Original proof that "almost all decision problems are uncomputable"? Who gave the original proof that "almost all decision problems are uncomputable"? Any hint at the original paper appreciated, thanks!
So the answer to my original question is the following: Because the statement is a corollary of the two facts that 


every program (Turing machine) is a finite binary string, i.e., a natural number,
every decision problem is a function $f: \mathbb{N} \to \{0,1\}$ and hence corresponds to a number $x \in [0,1)$ (and every such $x$ indeed encodes a meaningful decision problem, see Sasho Nikolov's first comment above)


the question about the original author / paper of this simple corollary is not that much interesting. (And the origins of the mentioned facts themselves I can trace back, of course.)

EDIT: I add here that this is the answer modulo the objection by Damiano Mazza (see in the comments above), which I need to check/think about first.