There's no context independent meaning and depending on the context it's useful to use different notions.
I personally distinguish emotional beliefs, probabilistic beliefs and logical beliefs.
The native encoding in which beliefs are stored in minds is emotional and most of the beliefs people hold don't have explicit probabilities attached to them.
When it comes to reasoning about well-defined events in a structured way, probabilities are very helpful.
I'm programming I don't ask myself about the probability that a certain variable might be null. If I consider it a plausible state for the variable to be null, I rather handle it in my code regardless of the probability that I attach to that event.