Technically black holes have an internal structure as they are simply a small area taking up a large mass, like squishing the entire mass of planet Earth down to the size of a pea, but I don't see probing a black hole as possible with our current technology. If an object has so much mass that objects moving at the speed of light do not have the force to escape its gravity, trying to send probes to it is impossible (also the area of a black hole is so small that probes would have to be microscopic to even be able to study it up close like a probe we'd send to the moon). But, that doesn't mean it's impossible. For example we can probe a black hole without going to it by using sensors of different types as well as telescopes. There are no nearby black holes so research on that level can only be done it miniscule amounts, but that doesn't make probing a black hole impossible.
