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I have difficulty understanding what I should do for this problem, can you help me? Specifically, I don't understand what probabilities I should start with given that the questions says I can't assume 0.9 to 0.1 probabilities. Maybe I'm wrong.

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Here's the calculator if you need http://psych.fullerton.edu/mbirnbaum/bayes/BayesCalc.htm

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You should start with $p=.50$. It says as much in the attached picture, quoted below.

He figures, instead, that there is about a 50/50 chance of being killed in a serious car accident whether or not one is wearing a seatbelt.

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