[asafira]

I don't think invoking quantum mechanics is necessary here honestly.

Let's say I flip a coin; most people would model the outcome as a p = 1/2 chance of heads and p = 1/2 chance of tails. This is fairly standard, of course, but I think it illustrates my point.

Of course, in reality there is only 1 outcome that's going to happen, but literally the best model of the system we can come up with, given our ignorance, is that it's 50/50 heads and tails.

So, what I am saying is that given that we know relatively little about the particle --- what it's average energy is --- we can come up with a probability distribution over states with that average energy that represents our "best guess" or "least biased" probability assignments.