Down the rabbit hole of pedantry: we don't need a distribution, just a measure, if we want to talk about how many reals it accepts. The Lebesgue measure is implied on the Reals if none is given, and the computable reals have measure zero.
We can't reasonably talk about a percent coverage, since the Lebesgue measure of the reals is infinite, but as a non-technical description, 'zero percent' is morally equivalent to saying it only covers a measure-zero set.
We can't reasonably talk about a percent coverage, since the Lebesgue measure of the reals is infinite, but as a non-technical description, 'zero percent' is morally equivalent to saying it only covers a measure-zero set.