If it happens to rain tomorrow, the picnic will probably be canceled.

Literal

By-chance tomorrow rain [subject-が] falls-[conditional-ば], picnic [topic-は] will-be-canceled [probably-だろう].

あす is the formal/written reading of 明日 ('tomorrow'), slightly more elevated than the everyday あした. The 万一+~ば+(passive)+だろう shape is a templated 'just in case [unlikely thing happens], outcome will probably follow' — a polite, hedging way to plan for contingencies.