The results before softmax don't sum to one so don't even act like a probability distribution. And that's the point. When you have the pre-softmax activations, there are infinitely many ways to convert them to something probability-like. You can normalize them after taking the square root, the square, raising to three, etc. Or you can exponentiate and for some reason that does better. Either way it's not a 'real' probability distribution.
That's the result after softmax. If you want to act on the raw results, you can still do that.