Why is my Custom Post Type not showing up after adding capabilities?

I’m trying to add a custom post types with capabilities, so a custom user role can do certain things with them. Eventually the custom role is a Client, and the post a Website, and I want clients to be able to log in and view their websites. However, the post type is not showing up as soon as I add capabilities => 'website'. Why is is not showing up? I was following this tutorial and here it seems to work at 3:54 (with vehicles as a custom post type).