"possibly" vs "probably"

[AquaMarine]

Business Idiom in English, Intermediate level

ESL/EFL Test #134 "Ways of thanking", question 7

How can I ......... thank you enough for all you've done?

(a) entirely
(b) probably
(c) possibly
(d) exactly

Business Idiom in English, Intermediate level

ESL/EFL Test #134 "Ways of thanking", answer 7

How can I possibly thank you enough for all you've done?

Correct answer: (c) possibly
_________________________

why "possibly" is the right choice here? how is it different from "probably"?

[Mister Micawber]

It is a set phrase: 'How can I possibly thank you enough?'
_________________
Native English teacher at Mister Micawber's