grammar - だろう in question context?

This is sentence:

「“見る”か。お前はいったい、どのような世界を“見て”いるのだろうな」

I'm not sure if this is really a question, but words like いったい and どのよう suggest that it probably is. So if this is really a question, then how should I inerpret だろう at the end, because usually as far as I know it represents information about which speaker thinks its almost certainly is true.

But here, it looks like question is in form of something like "In which way did you see world?", and I don't understand how だろう fits here.

Answer

だろう after an interrogative (いつ, 何, なぜ, ...) is something that may be called a "I-wonder marker". While ～ですか forms a question addressed to someone else, ～だろう forms a question addressed to yourself.

お前はいったい、どのような世界を“見て”いるのだろうな。
I wonder what kind of world you are "seeing".
I wonder what the world you are "seeing" is like.

どのように is "in what way" or "how", but どのような is "what kind of" or "like what".

More simpler examples:

• ここはどこだろう?
  (I wonder,) Where am I?


• ここはどこですか?
  (Please tell me,) Where am I?


• 誰だろう?
  (I wonder,) Who is it?