Probability measure of rank-$r$ matrices

Question

I have a question about the distribution of matrices with a specific rank. Consider $\mathcal{M}^{n\times m}$ the set of all $n \times m$ matrices with entries in some field $\mathbb{K}$. If I define a $\sigma$-algebra composed of the subsets of $\mathcal{M}^{n\times m}$, with a probability measure $\mu$ such that $\mu(\mathcal{M}^{n\times m}) = 1$, how to determine the measure $\mu(\mathcal{M}_{r}^{n\times m})$ of $m\times n$ rank-$r$ matrices?