Well, because any specific outcome from sampling a random distribution is indeed very unlikely.
In practice, that means that if you have an alternate "non-random" or "less random" explanation for the data, you'll be convinced that it's almost surely the correct one after just a few samples (via the obvious Bayesian decision framework, or just "common sense").
For example, imagine that you are rolling a die and 3 always comes up. On every roll, the likelihood of the die being a fair random die (as opposed to a loaded die) is divided by the number of sides, so with a 6-sided die, you'll usually be convinced that it's loaded after just 3-20 times of giving the same result (depending on your prior on it being loaded vs fair and your decision threshold).
Likewise, if only 1 and 2 come up you'll quickly be convinced that it's an unusual die that only has 1 and 2 symbols on the face.
Or another way to look at it is that processes are usually not random at all (rather they are usually deterministic, but the initial state is unknown) so a random distribution is a very bad model, and having any information about the initial state at all will drastically increase the likelihood and thus make the model with information strongly preferred; the likelihood of the random model is so low because that model is very bad, even though it may be the best available.
In practice, that means that if you have an alternate "non-random" or "less random" explanation for the data, you'll be convinced that it's almost surely the correct one after just a few samples (via the obvious Bayesian decision framework, or just "common sense").
For example, imagine that you are rolling a die and 3 always comes up. On every roll, the likelihood of the die being a fair random die (as opposed to a loaded die) is divided by the number of sides, so with a 6-sided die, you'll usually be convinced that it's loaded after just 3-20 times of giving the same result (depending on your prior on it being loaded vs fair and your decision threshold).
Likewise, if only 1 and 2 come up you'll quickly be convinced that it's an unusual die that only has 1 and 2 symbols on the face.
Or another way to look at it is that processes are usually not random at all (rather they are usually deterministic, but the initial state is unknown) so a random distribution is a very bad model, and having any information about the initial state at all will drastically increase the likelihood and thus make the model with information strongly preferred; the likelihood of the random model is so low because that model is very bad, even though it may be the best available.