Let $T$ be an expanding Markov map with countable number of inverse branches
and a repeller $\Lambda$ contained within $[0,1]$. Given a well behaved
non-negative potential $\phi$ we consider the set of points $x$ in $\Lambda$
for which $T^n(x)$ hits a shrinking ball of radius $e^{-S_n(\phi)(x)}$ around
$y$, where $S_n(\phi)$ denotes the n-th level Birkhoff sum, for infinitely many
iterates $n$. Let $s(\phi)$ denote the infimal value of $s$ for which the
pressure function $P(-s (\psi+\phi))$ is negative.