By definition of conditional probability,
[tex]\mathbb P(X|Y)=\dfrac{\mathbb P(X\cap Y)}{\mathbb P(Y)}[/tex]
If [tex]X[/tex] and [tex]Y[/tex] are independent, then [tex]\mathbb P(X\cap Y)=\mathbb P(X)\times\mathbb P(Y)[/tex], which reduces the above probability to
[tex]\mathbb P(X|Y)=\dfrac{\mathbb P(X\cap Y)}{\mathbb P(Y)}=\dfrac{\mathbb P(X)\times\mathbb P(Y)}{\mathbb P(Y)}=\mathbb P(X)[/tex]
This means the answer is the second choice.
