A man in his 50s and a 30-year-old woman were shot around 6 p.m. Thursday in the office of a law firm in Terrebonne, just north of Montreal.
Police said the shooting victims remained in critical condition.
Officers then discovered the bodies of the three men just after midnight Friday in a Boucherville home that had been set ablaze.
Longueuil police spokesman Tommy Lacroix said the bodies are likely those of a father and his two sons but he wouldn't confirm the information because the corpses had not been officially identified.
"What we know up to now is that one of the people inside the house — one of the victims — seems to have left the house at night and when he came back set the house on fire before committing suicide," Lacroix said.
Lacroix said investigators found a large quantity of fire accelerant in the home, leading them to believe the fire was set deliberately, "but that remains to be determined."
Police said it's too early to conclude a motive for the crimes but added they are not looking for any other suspects in the case.
Various reports said the father in Boucherville had filed a $1.2-million lawsuit against a lawyer who was one of the two people shot in Terrebonne.
The identities of the deceased were not made public and autopsies were ordered to determine the cause of death.