If we have
P($x_1,x_2,x_3$) $\propto$ $\delta_D$($x_1+x_2+x_3$-1) $\Theta(x_1)$$\Theta(x_2)$$\Theta(x_3)$,
then how to find the form of P($x_1,x_2,x_3$)?
i.e., how to calculate the integral $\int\int\int$$\delta_D$($x_1+x_2+x_3$-1) $\Theta(x_1)$$\Theta(x_2)$$\Theta(x_3)$ d$x_1$d$x_2$d$x_3$?
I have been confused about this question for a couple of days and really had no idea about it. Anyone can help me?