I'm struggling to find the right terms for what I mean (not a native speaker), maybe the word "transformation" is wrong in this context? I'm reading a paper which shows the following transformation / formula:
I'm having difficulties to understand why the two expressions are equal. I'm pretty sure that the nominator in the first expression is equivalent to the left nominator + right demoniator in the second expression. But I'm not sure why that transformation is valid, I would like to read about this law of transformation. I tried to search for "conditional probability transformation laws" but I do not find what I'm looking for. Can someone point me in the right direction or perhaps even explain the transformation?