  We prove the necessary and sufficient condition for the removability of the
fundamental singularity, and equivalently for the unique solvability of the
singular Dirichlet problem for the heat equation. In the measure-theoretical
context the criterion determines whether the $h$-parabolic measure of the
singularity point is null or positive. From the probabilistic point of view,
the criterion presents an asymptotic law for conditional Brownian motion.
