In a standard deck of 52 cards half are red and half are black. If you take a card with replacement, the 1/2 ratio remains constant. Each take is independent, so the probility for 3 takes is 1/2 × 1/2 × 1/2, or 1/8.
The 8 possible results are RRR, RRB, RBR, RBB, BRR, BRB, BBR and BBB. So you can see that 3 blacks, BBB, is one of eight, or 1/8