A magic cap doesn't turn you invisible as air. It doesn’t work that way. How I know? I used to have one.
Look there. Do you know his trade? Yes, a carpenter. And the woman with the top hat, she's a chimneysweep. You can tell just by looking at them, by their dress and their hats. The magic cap made it so you looked like someone you weren't - not a different face, just a different role. And most rich folks don't pay much attention to a stablehand.
No, I don't have it any more. Why? Now, that's a longer story.