There are numerous studies that show that our brain's natural way of thinking out probabilities is in terms of frequencies

Thinking about which probabilities?

Probability is a complex concept. The probability in the sentence "the probability of getting more than 60 heads in 100 fair coin tosses" is a very different beast from the probability in the sentence "the probability of rain tomorrow".

There is a reason that both the frequentist and the Bayesian approaches exist.