It's hard to see how revolutionizing our knowledge of how gravity works is going to lead to a return on investment.
UNLESS...they can keep it a secret until some fantastic new patentable technology is developed from this discovery. And if there is no discovery, and the Pioneer Anomaly turns out to be some ordinary effect, the investors are going to be out a lot of simoleons.
Private enterprise might do a good job of developing the probe for a government, or some big semi-public patron like a big research institute, but then it would get paid some pre-negotiated amount regardless of what the probe turned up.