A new puzzle about belief and credence

I present a puzzle about belief and credence, which takes the form of three independently supported views that are mutually inconsistent. The first is the view that S has a modal belief that p if and only if S has a corresponding credence that p. The second is the view that S believes that p only if S has some credence that p. The third is the view that, possibly, S believes that p without a modal belief that p. [Word Count: 85]