Perhaps specific context is required but what is the real meaning behind this phrase?

  • 1
    @user3856370 Strictly speaking, no. There is no "explanatory-の" in this sentence.
    – naruto
    Nov 8 '20 at 2:26

決まる means "to be settled" or "to be decided", and 決まっている means "has been (already) settled". But as a set phrase, (~に)決まっている also means "it goes without saying ~", "needless to say" or "certainly (although there is no direct evidence/guarantee)". See JLPT N2 Grammar: に決まっている

By extension, when used as the reply to a question, 決まっているだろう/決まっているでしょう effectively sounds like "Why ask?" or "Of course, ~" or sometimes even "That's a stupid question". You can think of this as a set phrase to memorize.

決まってんだろう is a contraction of 決まっているだろう:

  • 決まっているだろう: (literally) "It has been settled, hasn't it?"
  • 決まってるだろう: ("teiru → teru" contraction described here)
  • 決まってんだろう: ("ru → n" contraction)

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