While we are arguing semantics (and I agree that improbable would be a better word for the title) there is a difference. Improbable refers to odds. Probably impossible refers to odds of some binary outcome.
My winning the lottery is improbable. We all agree I have a shot at it, but it's very unlikely. But it's definitely not impossible, assuming it's not rigged.
Solving an NP problem with a P time algorithm is probably impossible. Either it can be done or it can't be. We suspect the latter, but we don't know 100%. Once we prove it one way or the other, it will will either be possible or impossible, in a binary sense.
My winning the lottery is improbable. We all agree I have a shot at it, but it's very unlikely. But it's definitely not impossible, assuming it's not rigged.
Solving an NP problem with a P time algorithm is probably impossible. Either it can be done or it can't be. We suspect the latter, but we don't know 100%. Once we prove it one way or the other, it will will either be possible or impossible, in a binary sense.