Fix a universal Turing machine $M$.
Let $A^*=\{0,1\}^n$ be the set of all binary string of length $n$.
Determine the Kolmorogov complexity $K(x)$ of each $x\in A$, w.r.t. $M$.
Just for a matter of simplicity assume that $K(x)'=\min(|x|,K(x))$.
Let $B^*=\{0,1\}^n$ be the set of all programs $y\in B$ of $T$: $x= M(y)$.
Now, suppose a parallel machine $M_p$ that can run each program $y\in B$ for each element in $A$, in parallel. So we can get the length of all the programs $y$ whose machine ended with the right string $x$, and take the minimum as $K(x)'$.
So, should I assume that the non-computability is due to the fact that some machines that has not ended jet whose inputs $y$ are less than the current minimal program will eventually halt? What's the probability of this?
Also, maybe a measure of complexity should include a minimal length with a probabilistic confidence? Say $P(K(x)\geq l)\geq p$?