Does it make sense to speak of probabilities only when you have numerous enough trials?

No, the math of probability theory still works if you take probabilities as subjective degrees of belief. That is the foundation of Bayesianity, but even the frequency interpretation depends on subjective ignorance — if you had full knowledge of all information influencing the outcome of a given trial, you wouldn't be doing the trial, because you could predict the result. It depends on isolating certain causal factors and mind-projecting them as "random variables". In reality, they're not random — you just don't know what they are — and you can talk about your degree of knowledge about the result of 1 trial just as well as 1,000,000 trials.