When working on a probability problem like this, it's important to define the problem precisely otherwise you run into a more complicated version of bertrand's paradox http://en.wikipedia.org/wiki/Bertrandparadox(probability).
There are many different ways to described the space of all rectangular matrices which might be intuitively seen as "level" or "equal". These might give different results. In short, you have to choose an algorithm for generating a "random matrix" of the type you're looking for, otherwise the question won't make sense.
Of course, once you have such an algorithm for generating a "random matrix" you can run a short monte carlo experiment to get the number numerically. Questions similar to the one you've asked here are, from what little I've read on the subject, asked in random matrix theory.
