Bernardo randomly picks $3$ distinct numbers from the set \(\{1,2,3,\cdots,7,8,9\}\) and arranges them in descending order to form a $3$-digit number. Silvia randomly picks $3$ distinct numbers from the set \(\{1,2,3,\cdots,6,7,8\}\) and also arranges them in descending order to form a $3$-digit number. What is the probability that Bernardo's number is larger than Silvia's number? The answer should be in the form \(\frac{k}{m}\) in simplest terms. Please calculate the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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