The probability distribution of states is a basic quantity, both in and out of equilibrium. The probability of a non-typical event, given by the free-energy in equilibrium is accordingly of great interest. We study extended diffusive systems with noise, with a current flowing through them. By combining simple models and a novel numerical method, we show that the probability of rare events is well captured by descriptions where a few variables replace the full field theory. A new effect is revealed, previously not known to exist in such systems. Conditions for this effect to exist are presented.