So the reason you are getting a different answer online is because you are likely just doing your odds of winning or rather just your win/los ratio which is far different from the actual probability.

The actual probability is based on the amount of balls in the game and your card. There is a specific calculation for getting the odds for when you then remove odds from the pool which is what you get online.

You could also simplify it and base it on which card you pick at which point it would be 1/x where x is the number of cards since there always has to be one person to win