A clinic classifies patients into three risk groups for a certain condition: High Risk ($20\%$ of patients), Moderate Risk ($30\%$), and Low Risk ($50\%$). The probability of testing positive for the condition is $0.80$ for High Risk, $0.15$ for Moderate Risk, and $0.02$ for Low Risk. If a randomly selected patient tests positive, what is the probability that they belong to the Moderate Risk group?