Sharing GDI and DirectX and Priority

I was wondering how these two coexist as different controllers of the same Windows UI and which are handled first?

To write DirectX code, you do not need to remove any Win32Api code, which may also contain GDI code, and nothing prevents you from calling GDI and Win32 functions. In fact, nothing is touching when interpreting the WM_PAINT message. So how do they work on the same surface? Will DirectX render what it should display and then GDI rendering on top, or vice versa, or is it random?