Two ordinary fair dice are rolled. A score of 3 points is awarded if exactly one die shows an odd number and there is also a difference of 1 between the two numbers obtained. A player who rolls two even numbers is awarded a score of 2 points, otherwise a player scores 1 point.

a. Draw up the probability distribution table for S, the number of points awarded.

b. Find the probability that a player scores 3 points, given that the sum of the numbers on their two dice is greater than 9.