Odds for a 1–1000 draw
There are 1,000 possible results, so each number has a 1 in 1,000 chance (0.10%) of being picked on any single draw. Each draw is independent: getting 1000 once doesn't make it more or less likely next time.
Pick several numbers at once
Change "How many numbers" to generate a list. Untick "allow duplicates" to get unique numbers, up to all 1000 in a random order.