Indirect interactions are widespread among prey species that share a common predator, but the underlying mechanisms driving these interactions are often unclear, and our ability to predict their outcome is limited. Changes in behavioural traits that impact predator space use could be a key proximal mechanism mediating indirect interactions, but there is little empirical evidence of the causes and consequences of such behavioural-numerical response in multispecies systems. Here, we investigate the complex ecological relationships between seven prey species sharing a common predator. We used a path analysis approach on a comprehensive 9-year data set simultaneously tracking predator space use, prey densities and prey mortality rate on key species of a simplified Arctic food web. We show that high availability of a clumped and spatially predictable prey (goose eggs) leads to a twofold reduction in predator (arctic fox) home range size, which increases local predator density and strongly decreases nest survival of an incidental prey (American golden plover). On the contrary, a scattered cyclic prey with potentially lower spatial predictability (lemming) had a weaker effect on fox space use and an overall positive impact on the survival of incidental prey. These contrasting effects underline the importance of studying behavioural responses of predators in multiprey systems and to explicitly integrate behavioural-numerical responses in multispecies predator-prey models.