You are in bed with your lover and you hear a car in the driveway. You say "Maybe it is my husband." or "It might be my husband." You do not say "He might be my husband."
Bottom line: "He" is not the subject of this sentence. In fact, there is no word, even implied, meaning "he" in the Czech sentence. (If the word "to" were deleted, then "he" could be the implied subject of the sentence. But that is not the case here. The "to" makes it clear that "it" rather than "he" is the subject.)
We're going for the most exact translations possible, rewording it only when the sentence wouldn't sound natural in English. :)
"Možná to je můj manžel." - "Maybe it is my husband."
"Mohl by být mým manželem/Mohl by to být můj manžel." - "He might be my husband."
My answer of "that might be my husband" was corrected to "that may be my husband." ...
what the difference betwene "probably" (which is somehow incorrect) and "possibly" (which is says that it is a right word)?
The Czech here means "maybe" or "possibly". It does not mean "probably". For the difference in the English words, see my earlier comment below.
probably is as good as possibly or maybe in this situation, I dont see any reason to state that "probably that is my husband" is wrong
The word "maybe" means something different from the word "probably". The word "maybe" means "possibly". The word "probably" means not just "possibly" but in fact "likely".
Words have actual meanings, both in English and in Czech. True, in the situation we are given, a speaker might have said "probably" rather than "maybe". Both utterances could be called realistic. But the fact remains that he/she said one, not the other.
"Probably" is on the list of possible translations at the link below, but it's pretty close to the bottom, which to me would suggest that it's not one of the better options. All the rest have a feeling of possibility, just like "maybe."