If we order all the positive computable real numbers $r_1,r_2,r_3...$ by their Kolmogorov complexity in some language $L$, then make a histogram plot of the $r_i$ on the real line, and we scale it such that the height at one point is constant, and let the bin-size go to 0, what can be said about the resulting distribution as $n\rightarrow\infty$? I'd expect it to approach something (very roughly) like the normal distribution.

Is there any nontrivial $L$ for which we know of a distribution that becomes apparent for large $n$?