There is a formal succession process, but it's been regularly sidestepped for various reasons. So you basically have a real-life Game of Thrones where your family aren't your loyal and trusted confidants, but the exact people you're paranoid of. And for very good reasons. For instance one Saudi king was assassinated by his nephew (who was later publicly decapitated), then his brother took the throne, and so on endlessly.
Who do you think MBS was purging in '17? Other royals. Rich royals. Competition for the throne.