When you probably can’t do something but don’t want to eliminate the possibility. Also, it is nicer than “probably not”.
My answer on if I can go is a solid maybe.
n. 1. Maybe. 2. Most-likely not. 3. Probably not. 4. Fat chance.
It's a solid maybe I'll be there, a soft perhaps... a wishful yes. On second thought, I can't make it. I have bowling that night.
When you are definitely don't want to commit to something but for sure want to have the option.
John: "Who is coming tonight?"
Marc: "I'll be there!"
Nathan: "I'm a solid maybe!"