"The total cost of [the Cassini-Hughes] scientific exploration mission is about US$3.26 billion, including $1.4 billion for pre-launch development, $704 million for mission operations, $54 million for tracking and $422 million for the launch vehicle."
http://en.wikipedia.org/wiki/Cassini–Huygens
Space probes are already cheap for what they accomplish. For comparison, we could have sent about 45 Cassini probes for what has been spent on the International Space Station (all costs in).
Private industry could do it way, way cheaper. SpaceX could probably build and launch 45 Cassini probes for what cost to do Cassini–Huygens.
Private industry can do a lot of things but a Cassini probe mission for $71 million all in seems unlikely in the near future.
NASA has a contract with SpaceX for 12 supply missions at $1.6 billion while NASA says a shuttle launch was about $450 million (but that figure probably doesn't include all the costs).
So SpaceX at this stage is at about 25-33% the cost of a space shuttle mission, but that's still a long way until we get to "45 Cassini probes" for $3.2 billion.