Conditional density of the second highest order statistics

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Notation:

$Y_1$: Highest order statistics of $(N-1)$ players' valuation.

$F_n^M:$ The distribution function of the highest $n$th order statistics of $M$ players.

$f_n^M:$ The density of the highest $n$th order statistics of $M$ players.

In Vijay Krishna's book "Auction theory", page $31$. It said that the density of the second highest valuation of $(N-2)$ players is

$f_2^{(N-1)}(y|Y_1<x)=\frac{1}{F^{(N-1)}_1}(x)(N-1)(F(x)-F(y))f_1^{(N-2)}y$

Would you please help me explaining this equation? And may I ask what books or materials should I learn to understand it?

Thank you very much for your time!