  In many practically important problems which rely on particles' transport in
realistic corrugated channels, one is interested to know the probability that
either of the extremities, (e.g., the one containing a chemically active site,
or connected to a broader channel), is reached before the other one. In
mathematical literature, the latter are called the "splitting" probabilities
(SPs). Here, within the Fick-Jacobs approach, we study analytically the SPs as
functions of system's parameters for dynamics in three-dimensional corrugated
channels, confronting standard diffusion and active Brownian motion. Our
analysis reveals some similarities in the behavior and also some markedly
different features, which can be seen as fingerprints of the activity of
particles.
