# Is it possible to manipulate event probability this way?

Looking at @Ingix's answer at this link, is it possible to have the following event manipulation?

X = find in A day 2,

Y = not find in A day 1,

Z = in A

$$\mathbf P(X∣Y\cap Z) = \frac{\mathbf P(X\cap Y∣Z)}{P(Y)}$$

Basically, I want to account for the event in A that he left out. However, I am not sure it would be actually like this, when Y and Z not not known to depend on each other.

$$\mathbf P(X∣Y\cap Z) = \frac{\mathbf P(X\cap Y∣Z)}{P(Y\mid Z)}$$

$$\mathbf P(X∣Y\cap Z) = \frac{\mathbf P(X\cap Y∣Z)}{P(Y\mid Z)}$$