Using field data from brushtail possums (Trichosurus vulpecula), we present a method for modelling wildlife detection probabilities. Whereas detection functions typically (e.g. for distance sampling) describe the probability of direct human observations of animal subjects, we adapted this approach for cryptic species where observation depends on animals being caught in traps. Specifically, we characterised the probability of individual brushtail possums being caught by leg-hold traps in an area of farmland and native forest in New Zealand. Detection probability was defined as the per-individual, per-trap, per-night probability of a possum being captured, and was modelled as a function of home-range utilisation. Radio-telemetry was used to define the home-range distributions of 18 possums, and a combination of scanning radio-receivers and movement-activated video-cameras recorded instances when radio-collared possums encountered and stepped on the trigger of leg-hold traps (inactivated by being wired open). We estimated a 5% chance of trapping individual possums with a single leg-hold trap located in the centre of their home range for one night (median value across possums). Furthermore, this probability decreased rapidly as a function of distance, so that at 120 m from the centre of the home range there was less than a 1% chance of trapping success per possum per night. The techniques developed in this study could be applied to a wide variety of species and sampling methods.