Probability is a prior assessment of the likelihood of a particular event occurring in the future, usually over a given period of time or in association with another event, such as the casting of a die.
The assessment of probability is based, broadly, on our experience of the world. Supposing you have observed (and remember having observed!) 100 swans, and that 3 of these swans were black while 97 were not black, you will assess that the probability of observing a black swan in the future is 0.03.
However, this relies on various assumptions. For example, in the example given, when deciding that the probability of a black swan is 0.03, you assume that all other things remain equal. For example, you are going to assume that there isn't anybody currently culling all black swans around where you are. Or that there won't be a flight of black swans landing all around you every time you will be looking for a swan in the future.
Given that your knowledge of the universe is at best minimal, assessing any probability can only be a very dodgy process. You could say that the probability of correctly assessing most probabilities is near zero. It works well, though, when you can afford to do something like a "controlled experiment", essentially whenever you can be confident that the domain observed will be somehow protected from perturbations and will therefore remain broadly similar to what it was during the critical period when you made the observations on which you based your assessment.
However, there are many cases where we are all very good at it. For example: what do you think is the probability that the water in the bottle on your kitchen table suddenly explodes? Well, yes, near, very, very near zero. If it ever did, we would rather suspect foul play than anything wrong with our assessment.
Assessing probability requires a domain of relevance. For example, assessing the probability of seeing God is an impossible task. We can assess the probability of getting a 5 when casting a die. The domain of relevance is the casting of a die. You may decide if you are talking about any die at all or one particular die. Whether you trust the die to be fair or whether you cast the die a number of times before to observe what it does. And you need to decide how many times you will cast the die in the future to observe the result at least once.
A probability of zero just means you don't have any good reasons to believe it will happen, all things being equal. The probability of my meeting with God or Aristotle is zero. The probability of my meeting in the flesh someone I never met before is not zero if I can assume that this person is alive and well, and is indeed living on this planet.
The probability of observing, during a given period of time, some event with a probability of zero is 1. This is because at best we only have a very partial knowledge of the world and our assessment of probabilities, however careful it might be, remains a dodgy business (even before taking Quantum Physics into account).
We don't usually pay attention to that because, essentially, we don't assess at all the probability of most of the least probable events, which are too many and insignificant for us to bother. Even if we count the assessment of probability we do without even thinking about it, there are still many possible events we won't assess. What is the probability of Donald Trump inviting himself in my home for dinner tonight? Well, I never thought of that one before, I must confess, even though on reflection, it's definitely not zero.
So, no paradox, I'm afraid. Probability is about predicting the future given what we think we know of the universe from our experience of it, which is necessarily very limited.
So, getting it wrong is... probably probable, more or less.