Step-by-step Solution:

\[ \textbf{Step 1: Total balls in the box.} \] \[ \text{Total balls} = 8 + 7 + 6 = 21 \] --- \[ \textbf{Step 2: Favourable cases (neither red nor green).} \] That means the ball must be blue. \[ \text{Number of blue balls} = 7 \] --- \[ \textbf{Step 3: Probability.} \] \[ P(\text{Blue}) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}} = \frac{7}{21} = \frac{1}{3} \] --- \[ \boxed{\tfrac{1}{3}} \]