Consider the discrete case:

Shannon's entropy is $H(x)=\sum\limits_i^n p(x_i) x_i$.

Probability based on prefix-free Kolmogorov complexity is $R(x_i)=2^{-K(x_i)}$ where $K(x_i)$ is the prefix-free Kolmogorov complexity of $x_i$.

What is the relation between $R(x_i)$ and $p(x_i)$?  Are they equal?

I remember vaguely that a book has discuss on the relation without any precise result.