"Mais ils n'ont pas de possibilités de gagner."
Translation:But they have no chance of winning.
Neither of the English sentences they provided are common. In English we say, "But they have no chance of winning" or "possibilities of winning." Possibilities to win is an awkward and literal translation. Duolingo did not accept my translation of "But they have no chance of winning."
I think the English sounds bad with "possibilities", but maybe I am being overly logical: if they have "no possibilities" to win, that means that it's not true that they have more than one possibility to win, but it doesn't exclude the case that they have exactly one possibility to win. Since the last is certainly not what's intended, I'd write this as "But they have no possibility to win".