Conceivably is possible Presumably is probable.

Presumably this has now been answered. Conceivably you may still have problems, but I doubt it.

“Conceivably” would be used more to imply something was… well, conceivable. Believable. It would be used more to show someone understood the concept of something. “Presumably” would be used more with someone’s opinion in mind, rather than whether it’s believable or not. For example, you would write, “Presumably, he had to change his clothes after falling into the river.” and “He couldn’t conceivably use his wet towel to dry off.” Presumably is more uncertain, used as a matter of “well, I IMAGINE this is how things are…” Whereas, conceivably more directly goes to how outright possible something is or isn’t. It’s less… opinionated, and more factual. Here’s hoping I answered your question even a little =)