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The predator–prey space game and the costs associated with risk effects are affected by prey 1) proactive adjustments (when prey modify their behaviour in response to an a priori assessment of the risk level) and 2) reactive adjustments (when prey have detected an immediate threat). Proactive adjustments are generally well‐studied, whereas the frequency, strength and duration of reactive adjustments remain largely unknown. We studied the space use and habitat selection of GPS‐collared zebras Equus quagga from 2 to 48 h after an encounter with lions Panthera leo . Lion–zebra encounters generally occurred close to artificial waterholes (< 1 km). Two hours after an encounter, zebras were more likely to have fled than stay when the encounter occurred in more risky bushy areas. During their flight, zebras selected grasslands more than usual, getting great visibility. Regardless of their initial response, zebras finally fled at the end of the night and reached areas located far from waterholes where encounters with lions are less frequent. The large‐scale flights (∼4–5 km) of zebras led to a local zebra depression for lions. Zebras that had fled immediately after the encounter resumed their behaviour of coming close to waterholes on the following day. However, zebras that had initially stayed remained far from waterholes for an extra 24 h, remaining an elusive prey for longer. The delay in the flight decision had different short‐term consequences on the lion–zebra game. We reveal that the spatial context of the encounter shapes the immediate response of prey, and that encountering predators induces strong behavioural responses: prey flee towards distant, safer, areas and have a constrained use of key resource areas which are at the heart of the predator–prey game at larger spatio‐temporal scales. Nighttime encounters were infrequent (once every 35 days on average), zebra responses were short‐lived (< 36 h) but occurred over a large spatial scale (several km).