Six distinct integers are picked at random from \(\{1,2,3,\ldots,10\}\). What is the probability that, among those selected, the second smallest is \(3\)? Express your answer in the form of \(\frac{k}{m}\), where the fraction is in simplest form, and find the value of \(k + m\).

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