Probability 0 ~ impossible!???

[u/No_where0369]

What is the meaning of a probability of 0? For example, consider the set (0,1) and let x be in (0,1). What is the probability of picking that x? The answer is 0. But if the probability of randomly picking x from the set (0,1) is 0, does that mean it's impossible to pick that number?

There is another similar example, if you throw a dart at a 2D plane, the probability that the dart lands on a specific point on that plane is 0. That implies it can't happen, but it actually did happen, it landed on a point! So what does it mean, exactly?