でしょう is a conjugated form of
です, and can also be seen in the contracted form
でしょ (more casual).
でしょう is regularly translated to ‘right?’, or ‘probably’ in English. In a broader sense it just expresses an assertion about something (like
です), that the speaker assumes the listener would probably agree with.
-
イタリアは良（よ）かったでしょう。
Italy was nice, right? (Has the nuance of ‘I bet!)
-
今日（きょう）の昼（ひる）ごはんはハンバーガーでしょう。
Today's lunch is probably hamburgers, right?
In the above, we can see that, in both examples, the speaker is looking for confirmation that/affirming that the listener agrees with them.
As
でしょう is a conjugation of
です (the polite form of だ), it usually follows the plain form of words, rather than words using ～ます. However, in very formal situations, or older literature ～ます
でしょう may be seen.
Despite sounding relatively low confidence, using でしょう implies that the speaker has some form of information that makes them believe that the (A) statement is true.