# Probability distributions based on Kolmogorov complexity?

Suppose a human being randomly chooses a real number $$x$$ with $$0. It seems the probability of choosing $$x$$ is closely related to the Kolmogorov complexity of $$x$$. That is, a number like $$0.1$$ or $$0.333...$$ which requires little information to specify has a high probability of being selected, while most reals between $$0$$ and $$1$$ are so complex they could never be specified by a human being, and thus have zero probability of being selected. Are there any probability distributions that formalize this sort of approach?

• Any countably additive probability distribution will have to assign $0$ probability to all but a countable set of possible :"random" selections. – Ethan Bolker Apr 24 '19 at 23:05