A quantum particle coupled to a quantised field behaves as if it were effectively heavier than its actual mass. Enhanced binding refers to the phenomenon that due to this effective mass of the particle, the system admits a ground state, unlike the uncoupled system. Feynman-Kac formulas allow for a probabilistic interpretation of the problem: one studies a pinned Brownian motion with a Gibbs-type reweighting. The reweighting incorporates two factors: a reward for paths that stay close to the origin and a reward for paths that look locally the same. The strength of the second reward is determined by a system parameter called the coupling strength. We are interested in the behaviour of the path at t=0 (taking the pinning at -T and T) for T large. Our main contribution is that for large enough coupling, these distributions do not vanish in a neighbourhood around 0. This can be interpreted as the particle localising, which implies the existence of a ground state in the quantum system. Joint work with Volker Betz and Mark Sellke.