Why Not
Pettigrew confessed to harry and co right.
well, in one of the books-i think its 4, snape talks about using his truth potion
couldnt the ministry either
give the potion to sirius and ask - did you betray the potters-did you kill peter
and couldnt they give it to harry hermione ron, lupin and say 'did pettigrew confess to it, what did he say'
techinically this would make sirius a free man