I suspect it depends on the implementation but it would help to know what you mean by that. E.g. is it an efficient UTM that outputs a distinct TM on all input strings, or is it something more lenient?

@gregrosent It's a traditional Turing machine, tape starts with all 0s.

@IsaacKing I meant how are you encoding the description of a Turing machine as a string.

@gregrosent I'm ...not? This is a question about the set of all Turing machines, not how to transcribe them.

@IsaacKing There are ℵ_0 Turing machines, of which ℵ_0 halt (i.e. implement a computable function) and ℵ_0 don't. ℵ_0/ℵ_0 isn't a well defined fraction, so the only interpretation of the question that makes sense to me is "Let M_1, M_2, M_3, ... be an enumeration of all Turing machines. What's the limit as n goes to infinity of the fraction of {M_1, M_2, ..., M_n} that implement computable functions (if the limit exists)?" I don't remember what I was thinking when I wrote the above comments, but looking at it now, it seems I was expecting M_i to be the output of a UTM applied to the binary representation of i or something like that (which seems like the most natural way of enumerating Turing machines).

@gregrosent Oh, enumerated in increasing number of states. Guess I didn't specify that anywhere, oops.