This question boils down to the statistical concept of calibration. A system that makes predictions (i.e. your friend) is well-calibrated if its probabilistic predictions are borne out by empirical evidence. Without knowing how well-calibrated your friend is, it is impossible to say if his estimates of probability are reliable. Certainly him stating a probability estimate doesn't make it so, we need more information about if those estimates are any good or not.
For example, if your friend makes the statement that he is 75% sure of something, and is actually correct 75% of the time of these predictions, he is well-calibrated in this range. On the other hand, if events that he predicts will happen with 30% probability actually occur 50% of the time, he tends to underestimate likelihood and is not well-calibrated.
If your friend is well-calibrated, then yes, his statements of likelihood are in fact very close to the true likelihood of an event occurring. If he is 99.7% sure of something, then he will only be wrong 3 times in 1000. However, if your friend is poorly calibrated, his estimates of likelihood don't really have any bearing on reality. He could be 99.7% sure of something and still have it occur 0% of the time.
You can test your friend's calibration with a simple online test, found at http://calibratedprobabilityassessment.org/. This tests asks a series of general knowledge questions. The goal isn't to answer them all correctly, but to correctly judge your confidence in your answers. For each question, you must select one of two options and rate your condfidence in the answer from 50-100%. A well-calibrated person will get roughly 60% of the questions right that they are 60% sure of, 80% of the questions right that they are 80% sure of, and 100% of the questions right that they are certain of.