2004 AMC 10A Problem 2

For any three real numbers $a,$ $b,$ and $c,$ with $b \neq c,$ the operation $\diamond$ is defined by $$\diamond(a, b, c) = \dfrac{a}{b - c}.$$ What is $\diamond(\diamond(1, 2, 3), \diamond(2, 3, 1), \diamond(3, 1, 2))?$