だろう

1. 1Expresses a conjecture or guess about something the speaker is not certain of ('probably', 'I think').Ex. 1
2. 2Spoken with rising intonation, it asks the listener to confirm or agree ('…, right?', 'isn't it?').Ex. 2

The conjecture sense is common in writing, such as essays and narration, and in plain speech. It is often reinforced by たぶん or きっと. The confirmation sense (だろう？/だろ？) belongs to casual conversation and can sound blunt or masculine. In polite speech, use でしょう instead.

• でしょうN5でしょう is the polite form of だろう; both senses and the way words attach to it are the same, and the conjecture meaning can be swapped depending on the situation. However, using rising-intonation でしょう？ to confirm with elders or superiors can still be rude—prefer ～でよろしいでしょうか.
• に違いないN3に違いない is close only to the conjecture sense of だろう; it expresses much higher certainty, usually with evidence, meaning 'it must be...'. It cannot use rising intonation to seek agreement. Its polite form is に違いありません.
• はずだN4はずだ is close only to the conjecture sense; it emphasizes that there is grounds and that something is logical, showing more confidence than だろう. It can also use はずだった to mean 'was supposed to', but cannot seek confirmation. When attaching, nouns take の and na-adjectives take な.
• かもしれないN4For conjecture, the attachment is the same and the two are interchangeable, but かもしれない expresses lower certainty—it only says something is possible, leaving room for doubt. It has no rising-intonation confirmation use, and its polite form is かもしれません.
• らしいN4らしい makes conjectures based on hearsay or external signs and can mean 'I heard', giving an objective, detached tone; だろう is the speaker's subjective judgment. らしい has no rising-intonation confirmation use, and it also has a suffix sense (e.g., 男らしい).
• ではないかN4To express conjecture, ではないか must be used as のではないか, which is softer than だろう; it can also express confirmation with a tone of discovery or surprise, and with the volitional form it can issue a call to action, which だろう cannot. It is relatively formal; in speech it becomes じゃないか.

でしょう is the polite counterpart of だろう; に違いない expresses much stronger certainty, はずだ an expectation based on logical grounds or known facts, and かもしれない a weaker possibility. らしい signals an inference from outside evidence or hearsay, while ではないか frames the idea as a negative question, either pressing a view or suggestion on the listener rhetorically or, often as ではないかと思う, voicing a hesitant suspicion ('I wonder if…').