Supposition doesn't need proof, but it's based on some reason or belief. Her supposition that the keys were in the car was correct, even though she hadn't checked.
Pro Tip 2/3
Likely True
A supposition is often something you think is true or likely, rather than a wild guess. His supposition that the traffic would be heavy at this hour was logical.
Pro Tip 3/3
Conversation Starter
Use supposition to introduce an idea you're not sure about but want to discuss. I'm working on the supposition that she'll be late, so let's wait a bit longer.