Here's a possibly useful intuition-adjuster for the "Tuesday boy" problem: replace "born on a Tuesday" with something much less probable. Pr(two boys | two children, one a boy who will one day be President of the USA) is "obviously" about 1/2 rather than about 1/3, because now you can (almost) meaningfully talk about "the other child", which you can't in the case of Pr(two boys | two children, one a boy). The less uniquely-identifying the extra information, the nearer you are to the original "two children, one a boy" scenario.

If you want to do the actual calculation, you might want this picture in your head: a 14x14 table of possibilities, boys in the first 7 rows/columns, Tuesday in the first and 8th row/column. "Two children, one a boy" excludes the bottom-right quadrant. "Two children, one a Tuesday-boy" excludes all but the first row and column.