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The connection between absorbing boundary conditions and hard walls is wellestablished in the mathematical literature for a variety of stochastic models,including for instance the Brownian motion. In this paper we explore thisduality for a different type of process which is of particular interest inphysics and biology, namely active particles. For a general model of an activeparticle in one dimension, we provide a relation between the exit probability,i.e. the probability that the particle exits an interval from a given boundarybefore a certain time $t$, and the cumulative distribution of its position inthe presence of hard walls at the same time $t$. We illustrate this relationfor a run-and-tumble particle in the stationary state by explicitly computingboth quantities.

Relating absorbing and hard wall boundary conditions for active particles