The word だろう is used in exactly the same way as でしょう. The only difference is that だろう is more casual than でしょう, in the same way as だ is more casual than です.
It will probably be sunny tomorrow. | 明日 は 晴れる だろう。ashita wa hareru darou. |
Your father is probably busy. | お父さん は 忙しい だろう。otousan wa isogashii darou. |
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