"I shouldn't wonder"

This is a set phrase. See, for example,

http://www.oxforddictionaries.com/us/definition/american_english/i-shouldn't-wonder

Is its preceding clause conditional or factual?

For example, in the sentence
It's paid for with stolen money, I shoudn't wonder.

Is 'It's paid for with stolen money' conditional or fact?

contrapositionIs 'It's paid for with stolen money' conditional or fact?

It is conjecture -- something the speaker believes to be likely.

Don't forget the spelling: shouldn't