でしょう

1. 1Conjecture: the speaker judges something to be probable but not certain.Ex. 1
2. 2Confirmation: with rising intonation, the speaker asks the listener to agree with something the speaker assumes is true.Ex. 2

Polite and common in everyday conversation and set contexts such as weather forecasts (明日は雨でしょう). In the conjecture sense it softens a statement, marking it as the speaker's judgment. In the confirmation sense it is spoken with rising intonation and often written with ？. The contracted でしょ sounds casual. Its plain counterpart is だろう.

• だろうN5「だろう」 is the plain form of 「でしょう」, with the same two meanings and the same connection rules, so for conjecture you can swap them to match the speech style. It is common in writing, news, monologue, or when speaking to people you know well or those junior to you, but it is inappropriate toward elders or in formal settings.
• じゃないかN4「じゃないか」 has no conjecture meaning and resembles rising-intonation 「でしょう」 only when confirming or seeking agreement, but it sounds more assertive and exclamatory and leans toward masculine speech. It can also follow the volitional form to make an invitation, which 「でしょう」 cannot.
• に違いないN3「に違いない」 overlaps only with the conjecture use of 「でしょう」 and is far more certain, expressing the speaker's strong, evidence-based conviction rather than the softness of 「でしょう」. It has no rising-intonation confirming use, and its polite form is 「に違いありません」.
• はずだN4For conjecture, 「はずだ」 emphasizes grounds in reason or common sense and is more confident than 「でしょう」, and 「はずだった」 can express an original expectation. It has no rising-intonation confirming meaning, and nouns take 「の」 and な-adjectives take 「な」 before it.
• ようだN4「ようだ」 resembles 「でしょう」 only in conjecture but focuses on judging from observation or sensation; it also has a figurative (simile) meaning and no confirming use. In the present form, nouns take 「の」 and な-adjectives take 「な」 before it, whereas 「でしょう」 attaches directly.
• かもしれないN4「かもしれない」 expresses only conjecture, with lower certainty than the conjecture use of 「でしょう」, meaning "might" and leaving more room for possibility; it has no rising-intonation confirming use. Neither pattern takes 「だ」 after nouns or な-adjectives.

だろう is the plain-style equivalent of でしょう, and じゃないか more strongly presses the listener to agree or recognize something. Compared with でしょう's general 'probably', に違いない expresses strong conviction, はずだ an expectation based on reasoning, ようだ an inference from observed evidence, and かもしれない a lower-certainty 'might'.