The compression code can be specified first. If you have a lot of data, the specification will be negligible in length, compared to the code itself. Together, the specification and the Shannon code give an upper bound on the Kolmogorov compmlexity. If this is the shortest known program, we may consider the Shannon code probabilities as our "best explanation" of the data.
You can also get posterior probabilities using a universal prior such as 2^-K(x), but of course, this can only be approximated in the limit of infinite runtime.
You can also get posterior probabilities using a universal prior such as 2^-K(x), but of course, this can only be approximated in the limit of infinite runtime.