Let's say someone enters a competition where the winner is select randomly. To enter you just post a comment. Now there are 1,300 entries and 17 prizes, so the chance to win a prize is 1/1,300*17*100 = 1.3%.
But if someone decides to cheat and posts 100 comments, hell have a 130% chance to win (100/1,300*17*100). How is that possible? If TotalComments - YourComments = >=17 then you have less than a 100% chance to win, because there is still the chance for any other 17 comments other than your 100 to be selected.
Can someone tell me where my calculation formula is wrong? If you didnt get the formula it's
nOfYourComments/nOfTotalComments * nOfPrizes * 100
If the cheater puts in $100$ tickets, then there is some chance he will win more than $1$ prize. That's where the math needs to change.
Your calculation ${100 \times 17 \over 1300} \approx 1.3$ actually shows the expected (a.k.a. average) number of prizes he would win. That's why it can be $> 1$. However, the fact that it is $> 1$ does not mean he will win something for sure. It's still possible the number of prizes he wins $= 0, 1, 2, 3, 4,\dots$
To calculate the probability he will win something, i.e. at least $1$ prize, you need a different method.
Any specific ticket will lose with probability $ = a = 1 - \frac{17}{1300} \approx 0.987$.
So probability that all of them lose $= b = a^{100} \approx 0.268$.
So probability that he will win something = $1 - b \approx 0.732 = 73.2\%$.