> I suppose you could prove it as much as any other feeling, by observing the way that people behave

Look up the term "philosophical zombie".

In a nutshell, you can simulate a conscious being using a non-conscious (zombie) being. It is possible to simulate it so well that an outside observer can't tell the difference. If this is true, then the corollary is that you can't really know if other people are conscious. You can only tell that you are.

For all intents and purposes I might be the only one who has consciousness in the universe, and I can't prove otherwise.