이었겠죠

must have been, was probably

→ 이다
이 to be + 었 Past tense + 겠 Future, intention, or conjecture + 죠 Polite sentence-ending (confirmation)
auxiliary · informal, past tense Rare #26,643
must have been, was probably A conjectural, polite form of 이다 used after a noun.
KO: 그때는 학생이었겠죠.
EN: I guess you were a student then.
Conjugation of 이다

분명 당신 이었겠죠

It must have been you.

— 프린세스 브라이드 (1987)

반복 재생 이었겠죠

It must have been on repeat, right?

— 추락의 해부 (2023)

형이나 아버지 같은 사람 이었겠죠

He must have been like an older brother or a father figure.

— 맨 프럼 어스 (2007)

물론 농담 이었겠죠

Of course you were joking.

— 러브 액츄얼리 (2003)