This kind of limit, called "convergence in probability" in mathematics, is incorrect and unreasonable to understand with the definition of limit in calculus.
Let's start with the conclusion: the limit of frequency is probability.
But the frequency is different from the frequency. The landlord should be confused. Frequency is the number of events. Frequency is the number of events divided by the total number of tests.
It has long been found that with the increase of the number of experiments, the frequency of events will stabilize near a constant, which is called "probability" to measure the possibility of time occurrence.