probability that a variable, as a function of choice variables, is among the top k out of n when ordered

Question

Suppose $(h_1,h_2,...,h_n)'$ is an $n\times 1$ vector.

Let $h_i=g_iX_i$, where $g_i$ is a choice variable which can vary across $i$ and $X_i$ is a random shock with Pareto Type I distribution.

$$f_X(x) = \begin{cases} {\alpha x_m^\alpha\over x^{\alpha +1}}, & \text{if $x\ge x_m$} \\ 0, & \text{if $x\lt x_m$} \\ \end{cases}$$ What is the probability, as a function of the choice variables, that any given $h_i$ will be among the top $k$ largest of the $n$ $h$'s?

Thanks very much.