P(r2 | r1) = P(r1 ∩ r2) / P(r1) = 2P(r1 ∩ r2) = 2∑P(n ∩ r1 ∩ r2) = 2∑(1/101 * n/100 * (n-1)/99) = 2/3.

Just expand conditional probabilities and use the law of total probability.

Intuitively, first pick red means the urn is more likely to be filled with red.