Predation is an important selective force on prey species, but avoiding predators can be costly. Efficient decisions on who to avoid (predator recognition) and when (situations with different predation risk) will determine the chances of prey survival. In coevolved predator-prey systems, detection of predator odours generally induces a response in potential prey to reduce predation risk. However, prey may not necessarily respond to odours of predators with which they have no previous experience, as predicted by the prey naïveté hypothesis. In turn, perceived predation risk may also modulate predator recognition and the intensity of antipredator responses. In this study, we investigate the responses of an introduced prey species, the European rabbit (Oryctolagus cuniculus), to odours from coevolved and non-coevolved, sympatric and allopatric predators in situations of high and low numbers of predators in Australia. We used pellet counts to quantify rabbits' use of space on experimental plots treated with predator odours. Rabbit avoidance of plots scented with coevolved predator odours was strongest, but they also responded to non-coevolved, marsupial predators. Predator abundance did not affect predator recognition in rabbits, although responses were more intense in situations where perceived predation risk was low and the intensity of responses decreased over time. Our results suggest that rabbits may have learned to recognize novel marsupial predators after 150 years of exposure in their introduced range.