The math, and the physical means of the draw. Because of the way the draw happens, you can conclude that every combination is equally likely, so long as there is no physical biases going on in the way the balls are drawn.
Now if we found out that some balls were heavier than others, or differently shaped, missing or something of that sort, then you can find that bias and combos would be more likely.
The best thing I can compare it to is a roulette wheel. So long as there is no bias in the wheel's shape, or the dealers spinning, the physical process to draw the game results in a normal distribution. In other words, it is fair and random every spin. No slots are gone, and the ball and wheel have no memory.
I guess it's mainly because I trust the Lottery to draw a fair game. As long as they are doing that, the math is simple. 56*55*54*53*52*46=175,711,536 equally likely combos. Because the balls are replaced and each draw is independent, this holds true everytime. If there was any other factor, like heavy balls, the math would become significantly more complex, and certarin combos would be more likely.
However, a game like Blackjack isn't like that. The odds are the same for the first hand of every deck. But after that, the deck's composition changes, so the odds do, as well. (B/C certain cards favor the house, and others the player, you can track what cards are left in play and bet bigger when there is an advantage. You don't have to do the math, just know the strategies. Someone else can do that math)
I don't really know how else to explain it. It's fairly simple. If the balls are all the same, just numbered, and are drawn by a random method, all the combos have the same odds. It's purely math and logic. There is nothing to suggest bias in the drawing, so the math has to be based off of unbiased draws. In an unbiased draw, every combo is equally likely to be drawn.
Plus, the only way to determine bias from an outsiders persepective would be to take a large sample size and run a statistical test on it. But there are less drawings than would be required for even a small confidence level. A roulette wheel takes about 20,000 spins to deteremine bias to a 99% confidence level. Imagine a Lottery.