(i) To find the probability distribution of \(X\), calculate \(X = R - B\) for each combination of red (R) and blue (B) spinner outcomes. The possible values of \(X\) are -2, -1, 0, 1, 2, 3. The probability distribution table is:

(ii) The variance \(\text{Var}(X)\) is calculated using:

\(E(X) = \frac{-2 \times 1 + (-1) \times 2 + 0 \times 3 + 1 \times 3 + 2 \times 2 + 3 \times 1}{12} = 0.5\)

\(\text{Var}(X) = \frac{(-2)^2 \times 1 + (-1)^2 \times 2 + 0^2 \times 3 + 1^2 \times 3 + 2^2 \times 2 + 3^2 \times 1}{12} - (0.5)^2\)

\(= \frac{26}{12} - \frac{1}{4} = \frac{23}{12}\)

(iii) The probability that \(X = 1\) given \(X\) is non-zero is:

\(P(X \neq 0) = \frac{9}{12}\)

\(P(X = 1 \mid X \neq 0) = \frac{P(X = 1 \cap X \neq 0)}{P(X \neq 0)} = \frac{\frac{3}{12}}{\frac{9}{12}} = \frac{1}{3}\)