1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$ 2. **Use the given information:** We know $$a - b = 2 \quad \text{and} \quad b - c = 2$$ 3. **Find $a - c$:** Since $$a - c = (a - b) + (b - c) = 2 + 2 = 4$$ 4. **Substitute values into the expression:** $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2} = \frac{2^2 + 2^2}{4^2} = \frac{4 + 4}{16}$$ 5. **Simplify the fraction:** $$\frac{8}{16} = \frac{\cancel{8}}{\cancel{16}} = \frac{1}{2}$$ 6. **Final answer:** $$\boxed{\frac{1}{2}}$$