But conspiracy charge just depends on overt act(s), so being convicted of conspiracy doesn't necessarily mean he was convicted on the basis that particular overt act occurred. The prosecution never had to prove all the overt acts, including murder-for-hire, were true to convict for the more generalized non-murder conspiracy. Just that some subset of overt acts were true.

> prove

There are different levels of proof. For example, civil court only requires a preponderance of evidence.