だろう isn't a guess — it's a ball rolled toward the other person

Where the picture shows up in だろう

1. 1

   rolled into the fog

   明日はたぶん晴れるでしょう。

   ashita wa tabun hareru deshō

   It'll probably be clear tomorrow.

   This is why forecasts always end in でしょう — they never nail it down.

2. 2

   rolled to yourself

   彼はもう知っているだろう。

   kare wa mō shitte iru darō

   He must already know.

   だろう is plain; でしょう is its polite form.

3. 3

   rolled over for agreement

   長旅で疲れたでしょう?

   nagatabi de tsukareta deshō

   You must be tired after that long trip.

   With a rising tone it becomes a warm read of how the other person feels.

4. 4

   set gently in their hands

   この書き方でよろしいでしょうか。

   kono kakikata de yoroshii deshō ka

   Would writing it this way be all right?

   でしょうか steps back one pace from ですか and sounds more deferential.

5. 5

   pointing back at a ball you rolled

   だから言っただろう。

   dakara itta darō

   See, I told you.

   Pushed as だろう? it turns confrontational — never aim it upward at a senior.