A pair of men with names matching those of American security contractors accompanied former auto executive Carlos Ghosn out of Japan after he was slipped aboard a private jet inside a large black case, typically used to carry audio gear, according to people familiar with a Turkish probe into the escape.

The plane took off from an airport near Osaka, Japan, on Sunday and landed in Istanbul Monday morning. Mr. Ghosn, who was awaiting trial in Tokyo, then took a car some 100 yards in heavy rain to a smaller jet that ferried him…

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