  For the one-dimensional Brownian motion $B=(B_t)_{t\ge 0}$, started at $x>0$,
and the first hitting time $\tau=\inf\{t\ge 0:B_t=0\}$, we find the probability
density of $B_{u\tau}$ for a $u\in(0,1)$, i.e. of the Brownian motion on its
way to hitting zero.
