Are there *3* interpretations of probability?

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In probability, we learn that there has two interpretations :

  • frequentist $P=\lim_{nb\ experiments\rightarrow\infty} \frac{favorable\ cases}{nb\ experiments}$

  • bayesian $P=$ degree of belief of the probability

Now, there is the formula that we learn at school : $P=\frac{favorable\ cases}{nb\ cases}$

is it an "interpretation" ? Is it a third one ? Is it the "classical interpretation of probability", as wikipedia tends to state ? https://en.wikipedia.org/wiki/Probability_interpretations

Does it has a relationship with the two others ?

Why are there only two interpretations in this other wikipedia : https://en.wikipedia.org/wiki/Probability#Interpretations

(remark, some authors call "classic" interpretation the frequentist one)