Used to make a strong assumption or supposition ('surely', 'no doubt'); often expresses the speaker's empathy or expectation.
大変だったでしょう。さぞかしお疲れのことだろう。
That must have been hard. You must be very tired.
さぞかし驚いただろう。
You must have been astonished.
合格したら、さぞかし喜ぶだろう。
If he passes, he will surely be delighted.