What was the outcome?: David did not know about Saul's death because he was not involved in it.
Saul and … Jonathan are also dead: Two other sons of Saul, Abinadab and Malkishua, were killed as well (1 Samuel 31:2). The Amalekite may not have known that Saul’s other sons had died. Or he mentioned only the son who could prevent David from ruling as king of Israel.