Winning more or Jackpot hunting

Sometimes a lucky jackpot winner finds out that he or she is not the only owner of the spoken for millions. Even with such large and totally tax free jackpots that are often won by people from nine European countries through the Euromillions lottery it is still quite bitter o realize that the prize sum will be divided into two, three or even more parts. This happens when more than one winner crossed out the same numbers in their lottery ticket. How does it happen at all? The probability of someone winning a lottery is fantastically scarce from the Math’s point of view, but the probability of several people winning simultaneously should be infinitely lower still, or not?