Armond Johnson Sr., 26, has been charged with aggravated murder in the killings and is being held in jail.
The two children whose bodies were found inside a house Tuesday died from smoke inhalation while their mother, Takeyra Collins, died from multiple gunshots at the home, authorities said.
Their neighbor, 35-year-old David Cousin Jr., was found fatally shot in a vacant lot near the house.
Police said Thursday that they believe Cousin was in the wrong place at the wrong time when he came across Johnson.
Court records don't list an attorney for Johnson. He is due in court Friday.
According to police, Johnson shot his 25-year-old ex-girlfriend, set fire to the home and then shot Cousin outside the house on Cleveland's east side.
A coroner identified the children as 6-year-old Armond Johnson Jr. and his sister, 2-year-old Aubree Stone.
Relatives have said Cousin and Collins were neighbors but didn't really know each other.
Johnson was initially arrested Tuesday on an aggravated robbery warrant when he joined grieving family members and friends outside the house after the bodies were found, Cleveland.com reported .
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