How does an extremely rare event unfold in a stochastic many-body system? This question has received much attention in recent years in the context of the large-deviations approach to nonequilibrium statistical mechanics. In this talk I consider a simple yet non-trivial example where such a question can be answered exactly, in a concrete model for mass transport – the zero-range process (ZRP). When conditioned on an atypical current, the typical behavior of the ZRP is found by complementary microscopic and macroscopic approaches. Extremely atypical currents are shown to necessitate the formation of real-space condensates. Surprisingly, these condensates form in the bulk, unlike condensation under typical conditions which can occur only at the boundaries.