Submenu feature add to existing menu

I have an existing menu, however I want to add a submenu to it. The existing menu is built as an unordered list <ul>, where each list element <li> contains a link <a>. The menu is contained in a <div> with a an id #menu to get styling and positioning. Attached is a mockup of the site with the current menu. The black box I have drawn, as well as its contents, is the submenu I would like - a black box having same width of the menu, with a three column design and a funnel coming from the hovered menu item.