The article is using probability where it really means proportion and prediction where it means evaluation. The mathematical equivalency is both much less surprising and less revealing once reframed.

If we consider the first example with the arithmetic code, the initial presupposition that only the characters A, B, and C appear in the string already reduces the entropy from 56 ascii bits to 14 bits (A vs Not A and B vs Not B for each character). If you further consider that you only need to distinguish B vs Not B if it's not A, then you can just represent As with a single zero bit and only represent the non-As as two bits (the first of which will necessarily always be a 1 bit). This gets you to 10 bits without even having the proportions of the string. Of course this would be a poor convention if there were say only a single A; in that worst case scenario you would need 13 bits, but simply knowing which character appears the most, without knowing by how much, 11 bits is the worst case scenario for a length 7 string with 3 potential characters. The last bit can be made implicit if you further choose the second conditional appropriately - i.e. if instead of B vs Not B we chose C vs Not C, our last bit would be zero and could simply be dropped meaning both 10 and a single 1 bit encode C - allowing you to encode the example string in just 9 bits and an arbitrary string of that length in 10, again regardless of proportions. That improvement over the arithmetic encoding result in the example is just a case of us cramming a little extra information into the encoding algorithm.

Arithmetic encoding is more clean and more easily extensible, it makes more sense to use than this custom encoding of 7 trits to binary but the point is the "probability" the article mentions is a superficial quality of life feature, not the secret sauce that is the actual key to compression.