To calculate the probability of winning a specific prize tier in a lottery game, first determine the number of ways you can match the required numbers for that tier. Then, find the total number of possible combinations of numbers that could be drawn. The probability is the ratio of the number of favorable outcomes (ways to win that prize tier) to the total number of possible outcomes. This involves calculating combinations for both the winning and non-winning scenarios and dividing the number of favorable outcomes by the total number of possible combinations.