off-chance

小説Ringに出てくる登場人物も増えてきたので次ぎの個所にでてくる人を簡単に紹介します。Yoshinoは主人公のAsakawaと同じ新聞社に所属する同僚（先輩？）で、Asakawaの謎解きのサポートをしています。 "she" と言うのは厄介なビデオを作ったと思われるSadakoで、IkumaはどうやらSadakoの父のようです。
There was nothing in Yoshino's report to suggest that she had squared off against her father. Rather, he got the impression that she was close to her parents. Asakawa suspected it would be impossible to discover the identity of this man. Nearly thirty years had undoubtedly changed his looks considerably. Still, just on the off-chance, maybe he should ask Yoshino to dig up a photo of Ikuma.
"off-chance" は可能性が低いとの意味だと思いますが、初めて見る表現なので辞書で確認します。
・Collins Dictionary: a small and unlikely possibility ⇒ In a public place there was an off-chance they might get caught.
・Wiktionary: (idiomatic) A condition of not being likely or probable.: He submitted a job application on the off chance that nobody better would.
・Cambridge English Dictionary: hoping that something may be possible, although it is not likely: I applied for the job on the off chance, but I didn't seriously expect to get it.
最後に引用した辞書のニュアンスがRingで使われている "off-chance" に近いようですね。
私が宝くじを買うのもこの "off-chance" に賭けているのです。