It does in fact exist. One great example of where nothing exists is between an atoms nucleus and its electrons. The space between it is absolutely nothing, no energy is small enough to exist inside the space, nor any particle small enough to fit inside it either. Hence, nothing is there.
It exists in the sense that anything does. We define it to be. Does a treble ready exist? Well only because we define something of th hat apparent solidity and shape as a table. I defineg what's in a jar after I take everything out of it, as NOTHIING. Wouldn't you?
Nothing is a word we made up so we wouldn't have to do something. What are you feeling? Nothing. What do you want to do today? Nothing. Are you okay? Ya. It's nothing. There is always a feeling. There is always a thought. If you ask," What's over there?" And you answer,"Nothing.", it just means that you are not interested in things over there. There will always be oxygen, air, life, carbon dioxide, gas, or anything.