だろう and でしょう

Probably
Noun/Adjective/Verb + だろう/でしょう。

だ and です also have a volitional form:

• だ→だろう
• です→でしょう

Usages

Unfortunately, だろう and でしょう don’t mean the same thing ましょう does.
There’s a lot of different meanings for だろう and でしょう, but for now we’re only going to talk about 3:

• Probability: – Most common usage, Flat intonation
• Confirmation: Somewhat common, “question” intonation.
• Criticism: Technically confirmation used in a mean way. “question intonation”. 

Probability

Most of the time, だろう・でしょう indicates probability.
If you learn only one of the meanings here, learn this one.

Examples

• 子供はなくでしょう
  The child will probably cry.
  
  
• 明日はさむいでしょう
  The weather will probably be cold tomorrow.
  
  
• そとはあついだろう。
  It’s probably hot outside. (If you don’t know)
  
  

Confirming an opinion

It can also be used to confirm your opinion or expectation with someone else.
Usually based on your own experiences or expectations. Usually readily apparent. Similar to ね

Examples

• そとはあついだろう。
  It’s (so) hot outside, right? (If you do know)
  
  
• よるはしずかでしょう
  It’s (so) quiet at night, isn’t it?
  
  
• そのみせ、おいしかったでしょう？
  That restaurant was good wasn’t it?
  
  

Criticizing

Lastly, でしょう can also be used to chastise someone. It essentially says “I thought you were a..”
This pattern is very critical of the other person.

Examples

• なんで泣いている？大人でしょう？
  Why are you crying? You’re an adult right?
  
  
• ともだちをなぐっていいですか？もう7さいでしょう？
  Is it ok to hit your friends？ You’re already 7 years old right?