If the website gets over a million uniques a day, there will be a new winner every day.
Do you roll a random number from a generator until it matches the displayed number?
If yes, if you have 1,000,000 visitors per day, the probability of having a winner is around 63 %.
However, if your random number generator guarantees that each player gets a different number then yes, the probability of having a winner approaches 100% as you get closer to the millionth visitor.