Accused of Cheating during an online exam
If you truly did not cheat then there will be a way to prove your innocence because false claims eventually lead to contradictions. The statistics aren't very threatening because it sounds like your accuser is probably assuming that each multiple choice question is a random event to get a ridiculous probability,  but that's nonsense. Exams are written to be answered correctly by those that are prepared. Thus in reality we expect many of those questions to be answered correctly and identically. You can offer to justify your answers to show you answered them on your own.

The identical submission time is concerning, but there is no reason to assume Blackboard is a perfectly coded software. Even programs like Microsoft Excel that are written by experts and probably used by millions have silly bugs in them. If I coordinated with my friends to the best of our abilities we could never click the submit button with identical submission times because we have different response times. If anything the identical submission time better supports there being a bug with blackboard than anything else. You should ask the accuser to explain how the identical times is evidence that you cheated and not that there was a bug with blackboard or any other aspect of online examination. You should also ask your accuser for how long have they been doing examination like this because likely it's new to them and they should be reminded of that.

Good luck.