So here is the explanation why the chance for winning the power ball is not 1 in 26.
From their web.
Sure, the odds of matching 1 red ball out of 26 are 1 in 26, but we are not giving the odds for matching a red ball. We give the odds for winning a prize for matching one red ball ALONE. If you match the red ball and one or more white balls, you win some other prize, but not this prize. The odds of matching one red ball ALONE are harder than 1 in 26 because there is some risk that you will also match one or more white ball numbers - and then win a different prize.
Some persons who enjoy statistics (they do really exist) will come up with odds of 1 in 17 billion for the jackpot prize. Remember that you don't need to match the numbers in exact order - we use combinations to determine the probabilities for the first five white balls and not permutations.