You explain that following au cas où, you would be tempted to use the subjunctive, but must use the conditional, but you do not say why?
As so many times when learning a language, there's no reason. It's just the way things have evolved over time.
To supplement Chris's answer:
Once upon a time, there were a few French expressions "en cas que, au cas que" which used Le Mode Subjonctif, although they've now become archaic. These expressions have been entirely substituted with "au cas où" which is always followed by Le Mode Conditionnel. See here: https://www.academie-francaise.fr/au-cas-ou-tu-seras
Also, Le Mode Subjonctif implies an uncertainty (doubt / hypothesis etc) while le Mode Conditionnel also implies a hypothesis (hence, an uncertainty too). Therefore, it would be naturally to assume that Le Mode Subjonctif would be used after "au cas où". Unfortunately, it isn't the case.
I hope this is helpful.
Bonne journée !
Merci de vos réponses rapides. Ken
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