A parking lot has $16$ spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers choose spaces at random from among the available spaces. Auntie Em then arrives in her SUV, which requires $2$ adjacent spaces. What is the probability that she is able to park? Express your answer in the form \(\frac{k}{m}\), where the fraction is simplified, and provide the value of \(k + m\).

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