The probability interpretation conjecture for normalized solution lengths

Let $N_U$ be the space of solutions on $U$, and let $\widehat{L}(\psi|_U)$ be the normalized length defined in the source from averaged extensions of the signal function. Define the proposed probability by

$$P(\psi|_U)=\frac{1/\widehat{L}(\psi|_U)}{\sum_{S\in N_U}1/\widehat{L}(S)}.$$

Probability interpretation conjecture. This quantity equals the real probability that the solution occurs.

The claim is part of an informal probabilistic interpretation of externally induced noise and normalized solution lengths. No mathematical or empirical justification is supplied.