  We show that the distribution of times for a diffusing particle to first hit
an absorber is \emph{independent} of the direction of an external flow field,
when we condition on the event that the particle reaches the target for flow
away from the target. Thus, in one dimension, the average time for a particle
to travel to an absorber a distance $\ell$ away is $\ell/|v|$, independent of
the sign of $v$. This duality extends to all moments of the hitting time. In
two dimensions, the distribution of first-passage times to an absorbing circle
in the radial velocity field $v(r)=Q/(2\pi r)$ again exhibits duality. Our
approach also gives a new perspective on how varying the radial velocity is
equivalent to changing the spatial dimension, as well as the transition between
transience and strong transience in diffusion.
