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だったろう

must have been, was probably

→ だ
だっ Past copula + た Past tense + ろう Conjectural
auxiliary · informal Rare #28,250
must have been, was probably Used to guess or infer something about the past; often conveys empathy in questions or comments.
JA: 昨日は大変だったろう。
EN: Yesterday must have been hard.
Conjugation of だ
Irrealis
だろうだったろう

大変だったろうに

You must have had a hard time.

— 風の谷のナウシカ (1984)

そして全くその通りだったろうと私も思います。

And I think that was exactly right.

多分、だめだったろう。

It probably didn't work out.

ずっと味方だったろう

You’ve always been on my side, haven’t you?

— Article 15 (2019)

大変だったろう

That must have been tough.

— ニュー・シネマ・パラダイス (1988)

君はアイオワが…嫌いだったろう？

You hated Iowa, didn’t you?

— フィールド・オブ・ドリームス (1989)

本を書くのにとてもいいネタだったろう？

That must have been great material for a book, right?

— ジョジョ・ラビット (2019)