= Solution
Uniform <sampling without replacement> is equivalent to revealing a uniformly random <permutation> of seven labelled balls. Each draw <position> is equally likely to contain any label, so its colour has the original proportions. Thus
$$
\boxed{\mathbb P(W_1)=\frac37,\qquad
\mathbb P(B_2)=\frac47,\qquad
\mathbb P(W_3)=\frac37.}
$$
For example the <law of total probability> gives $\mathbb P(B_2)=(4/7)(3/6)+(3/7)(4/6)=4/7$. Equal marginal <probabilities> express <exchangeability>, rather than <independence> between successive draws.
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