Various degrees of certainty

In general, Japanese people don't assert themselves of something unless they are absolutely sure that it is correct. This accounts for the incredibly frequent use of 「～と思う」 and the various grammatical expressions used to express specific levels of certainty. We will go over these expressions starting from the less certain to the most certain.

Using 「かもしれない」 to express uncertainty

「かもしれない」 is used to mean "maybe" or "possibly" and is less certain than the word 「多分」. It attaches to the end of a complete clause. For noun and na-adjective clauses, the declarative 「だ」 must be removed. It can also be written in kanji as 「かも知れない」 and you can treat it the same as a negative ru-verb (there is no positive equivalent) so the masu-form would become 「かもしれません」. In casual speech, it can be abbreviated to just 「かも」. There is also a very masculine version 「かもしれん」, which is simply a different type of negative verb.

Examples

（１）　スミスさんは食堂に行ったかもしれません。- Smith-san may have gone to the cafeteria.
（２）　雨で試合は中止になるかもしれないね。 - The game may become canceled by rain, huh?
（３）　この映画は一回見たことあるかも！- I might have already seen this movie once.
（４）　あそこが代々木公園かもしれない。- That might be Yoyogi park over there.
（５）　もう逃げられないかもしれんぞ。- Might not be able to escape anymore, you know.

Using 「でしょう」 to express a fair amount of certainty (polite)

「でしょう」 is used to express a level of some certainty and is close in meaning to 「多分」. Just like 「～です／～ます」, it must come at the end of a complete sentence. It does not have any other conjugations. You can also replace 「～ですか」 with 「～でしょうか」 to make the question sound slightly more polite and less assuming by adding a slight level of uncertainty.

Examples

（１）　明日も雨でしょう。- Probably rain tomorrow too.
（２）　あなたは、学生さんでしょうか。- Are (you) student?
（３）　これからどこへ行くんでしょうか？- Where (are you) going from here?

If you want to sound really, really polite, you can even add 「～でしょうか」 to the end of a 「～ます」 ending.
（４）　休ませていただけますでしょうか。- May I receive the favor of resting, possibly?

Using 「でしょう」 and 「だろう」 to express strong amount of certainty (casual)

The casual equivalent of 「でしょう」 is surprisingly enough 「でしょう」. However, when you are speaking in a polite manner, the 「でしょう」 is enunciated flatly while in casual speech, it has a rising intonation and can be shortened to 「でしょ」. In addition, since people tend to be more assertive in casual situations, the casual version has a much stronger flavor often sounding more like, "See, I told you so!"

Examples

（１）　あっ！遅刻しちゃう！- Ah! We're going to be late!
（２）　だから、時間がないって言ったでしょう！- That's why I told you there was no time!

（３）　これから食べに行くんでしょ。- You're going to eat from now aren't you?
（４）　だったら？- So what if I am?

（５）　掃除、手伝ってくれるでしょう。- You're going to help me clean, right?
（６）　え？そうなの？- Huh? Is that so?

「だろう」 means essentially the same thing as 「でしょう」 except that it sounds more masculine and is used mostly by males.
（A）　アリスはどこだ？- Where is Alice?
（B）　もう寝ているだろう。- Probably sleeping already.

（A）　もう家に帰るんだろう。- You're going home already, right?
（B）　そうよ。- That's right.