It must have rained during the night.

Literal

Night [gen-の] interval-during surely rain [subj-が] fell [nominalizer-の][probably-だろう].

An inference about overnight rain delivered as a confident conclusion: きっと ('surely') + ~のだろう ('it is probably the case that'). The reasoning behind the guess (puddles, wet road) is left implicit. Stripping evidence away like this is common in Japanese — speakers state the conclusion alone and trust the listener to fill in the cause.