Why does Piggy conclude that no one will know where they are?

Early in the first chapter of Lord of the Flies, Ralph seems unconcerned about being rescued since he has so much faith in his father, who is a commander in the British navy. "When he gets leave, he'll come here and rescue us," Ralph tells Piggy. But Piggy is more realistic.

"How does he know we're here?"
Because, thought Ralph, because, because...
"They'd tell him at the airport."
Piggy shook his head...
"Not them. Didn't you hear what the pilot said? About the atom bomb. They're all dead...
"They're all dead," said Piggy, "an' this is an island. Nobody don't know we're here. Your dad don't know. Nobody don't know--
"We may stay here till we die."

Piggy is under the misapprehension that the atom bomb has killed many (if not all) of the British troops and sailors. Despite this misunderstanding--and his bad grammar--he is aware that no one could possibly know the boys have survived and are stranded on the island. He expects to be there a long time.