\begin{align*} P(\text{kth as first}) & = P(\text{LL...LA})\\ & = \frac{13 \cdot 12 \cdot ... \cdot (15-k) \cdot 2}{15 \cdot 14 ... \cdot (16-(k+1)) \cdot (16-k)} = \frac{2 \cdot (15-k)}{15 \cdot 14} \end{align*}