It's even deeper than that. No uniform probablity distribution exists for the whole line (or plane, etc.). Nor does a uniform distribution exist on the integers. Otherwise, if challenged to "pick a number" one would usually pick a number that takes longer than the age of the universe to write down.
Still, tortoise's suggestion that the chance of this point in meta-space we are all part of right now being equivalent to any other point in meta-space infers that we are in a such a meta-space. That is the rub. His and your apriori of a belief system. Are we? Can't prove it.
Comes back to the fifty coins on the table. All heads after a toss -- what's on their other face?
What is most logical to say?