Substitute Cayenne Pepper for Black Pepper
You can't really substitute cayenne pepper for black pepper. They're completely different, not even in the same botanical order. Cayenne pepper is a powdered chile. Black pepper is tiny drupe. The heat in cayenne pepper comes from capsaisin, and the pepperyness in black pepper from piperine.

Closer substitutes would be white peppercorns (in moderation!), green peppercorns, red peppercorns or grains of paradise.

Of course, you still could use cayenne, but the taste would be as different as if you were to substitute it with allspice, or cumin, or some other spice. If you were to substitute it with cayenne, there's not really any ratio that is applicable, you would have to add it to taste.