Suppose $X \in \{0,1\}^{n \times m}$ is a matrix generated according to the following generative process: $$Z_{ij} \sim \text{Bernoulli}(p) \implies X_{ij} = \frac{Z_{ij}}{\sum_{k=1}^m Z_{ik}}.$$

Is there a name for the distribution of $X$? Is there a closed-form for $E[XX^\top]$? I am struggling to find any information on the behavior of this random matrix.