Kuan, the distribution will be anything but "normal." I think you mean "equiprobable," if that's even a word.

Also, what you mean to say (I'm sure) is not that the spot will be hit once in every 35 turns, but that in the long run, the spot will be hit 1/35 of the time.

In theory, you will eventually win against any nonzero odds with probability one. But of course, not only will you not likely live long enough to achieve this, but the lottery in question probably won't either.

Let me add that probability one does not mean the same thing as "it will happen." It means that the probability measure of it "not happening" is zero. These are close, but definitely not the same thing.