If you have trouble understanding where it comes from, stick with the raw numbers:

(Any first card, or 52 out of 52) and (a non-pairing second card, which is 48 cards out of the remaining 51)
(52/52) * (48/51)
.9411765
94.11765%

100 times in a row:
.9411765 * .9411765 * .9411765 * [. . .] * .9411765
.9411765^100
.002329
.2329%