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One reason you're getting different answers from different people is that the question can be interpreted in different ways, and it isn't clear what you mean by "probability" here. One way to make sense of the question is to assign priors and reason using Bayes' rule as in Matthew's answer.

Before asking for probabilities, you have to decide what's modeled as random and what's not. It's not universally accepted that unknown but fixed quantities should be assigned priors. Here's a similar experiment to yours that highlights the problem with the question:

Assume $$X_i$$, $$i = 1, \dots, 1000$$ are i.i.d. Bernoulli random variables with success probability (mean) $$p = 0.5$$. For interpretability, let's think of the $$X_i$$ as coin flips. Suppose you observe (the sufficient statistic) $$\sum_{i = 1}^{1000}X_i = 900$$. What is the probability that the coin is fair?

From a frequentist perspective the question is either nonsensical or the answer is "one". If you're Bayesian maybe you want to assign a prior distribution to $$p$$, in which case the question makes sense. The fundamental difference between my example and the question is that $$p$$ is unknown in the question, and the question disguises the fact that the actual randomness is whether a (presumably randomly sampled) person answers that the car is blue or not. The car's color is not randomly assigned and thus it's uninteresting to speak of the probability of it being blue from a frequentist perspective.