For the sequential case:

P(2 boys | >= 1 boy) = P(>=1 boy | 2 boys) * P(2 boys) / P(>= 1 boy)

where P(>= 1 boy of all 2 kids): 1 gg + 1 bg + 1 gb + 1 bb: = 3/4

P(2 boys): 1 gg + 1 bg + 1 gb + 1 bb: = 1/4

and trivially P(>= 1 boy | 2 boys) = 1

So P(2 boys | >=1 boy0 = 1 * (1/4) / (3/4) = 1/3