The odds are 1 in 1000. If I flip a coin, the odds are 50/50 (Well technically 49/51, but let's ignore that and call it 50/50).
That doesn't mean that if I flip it twice I'll have a heads and a tails, just in the same way that you won't see every number show over 1000 draws. The chance of you having one heads and one tails is 50%, while there's a 25% chance of either two head OR two tails.
The same can be applied to Pick 3, understanding that the odds are 1 in 1000, but also do the math and figure out the odds that any specific number will show within, say, 1000 draws. Of course that math you be harder because there's countless of ways 1000 pick 3 draws can happen, but it's still an finite amount of results.
The odds are always 1 in 1000 if you buy ONE STRAIGHT ticket. Otherwise it's x/1000 depending on how many straights you have covered (a box counting as 6 straights).
If you bought every combination, you have a 1000/1000 or 100% chance of losing half of your money. Degrees of certainty are not the same as odds. They are more like long term odds of specific events. And still, if you wanted to refer to degrees of certainty, the odds for any number over X amount of draws will be better than 1 in 1000. In fact, for 2 draws, I can say the odds of it showing at least once are....
(2/1000)-(1/1000000) or 1,999/1,000,000.
Of course, it just gets more and more complicated, and so it's not really something I'd want to do.