Prohibition of false prayer

Hello Rabbi,
In the Mishnah Berachot 9:3 it is written:
The former one who shouts, is this a vain prayer? How? His wife was from a faraway land, and he said, "May my wife give birth to a son," is this a vain prayer. He would come on the road and hear a sound of shouting in the city, and he would say, "May these not be the sons of my household," is this a vain prayer.
This means that even if there is a lack of knowledge, the prayer is still called a false prayer. The question regarding prayers today, assuming that the world operates according to natural laws, is there no prohibition of false prayer in all prayers? For example, if someone who is sick prays that he will recover, then this is as predictable as the birth of a male after conception, because according to the laws of nature, given the initial state of his body, the final state is deterministic. If we say that this also depends on his freedom of choice and that of his environment, then this freedom is not in the hands of God, and therefore this is again a false prayer. Of course, it is possible to say that God will intervene in the laws of nature (perform a miracle) and influence his recovery, but the same can also be said about the case in the mishna that God will change the sex of the fetus from female to male while it is in its mother's womb. So the question is, why are the regular prayers today considered legitimate prayers, while the prayers mentioned in the mishna above are considered false prayers? What is the difference between them?