〜でしょう
probably, …right?
Plain form + でしょう (casual: だろう)
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でしょう after a plain form makes a guess: 明日は雨が降るでしょう, "it'll probably rain tomorrow". It's what weather forecasters say every night.
After nouns and な-adjectives it replaces です directly: 学生でしょう, "(they're) probably a student".
With a rising tone it checks that the listener agrees: おいしいでしょう? "it's good, isn't it?" That's more insistent than ね.
でしょうか is a soft, polite question: 駅はどこでしょうか, "I wonder where the station is?" The casual version of the whole family is だろう (for guesses) and でしょ (for checking).
Examples
明日は雨が降るでしょう。
It'll probably rain tomorrow.
田中さんはもう家に帰ったでしょう。
Mr Tanaka has probably gone home already.
このケーキ、おいしいでしょう?
This cake's good, isn't it?
明日はたぶん晴れるだろう。
It'll probably be sunny tomorrow.
すみません、駅はあちらでしょうか。
Excuse me, would the station be that way?