First, we need to deal with the fact that there isn't a blackhole anywhere close. The closest is probably several thousand light years away. Basically, any blackhole is considerably beyond our reach. This is all before we can consider designing a probe that could somehow survive the trip there and then the immense gravity of the blackhole. Lastly, any information we could possibly gather would itself be trapped by the gravity of the blackhole.

TLDR: The distances are too great, nearly impossible to send the probe beyond the event horizon, and the information itself would be trapped with no escape.