Suppose $K_1$ is a local field and $K_2$ is a totally ramified finite Galois extension. Let $e$ be a positive integer with $[K_2:K_1]|e$. Consider the set of isomorphism classes of $K_1$ extensions of degree $e$ totally ramified, equipped with the probability coming from Serre's Mass formula. My questions are
1) What is the probability that an extension contain $K_2$? Substituting Serre's formula for $K_2$ in $K_1$ I don't get nothing nice, so I want to understand if I am doing some silly mistake in the computations with the conductor or if there is really no nice expression.
2) On the extensions of $K_1$ lying over $K_2$ I can consider the measure obtained by restricting the measure of $K_1$ and dividing out by the result of 1), and I can consider the measure coming from $K_2$(in other words the probability obtained by conditioning by the event 'lying over $K_2$'). Is the result the same?
EDIT: I was indeed doing a silly mistake using the wrong formula! It comes out pretty easily. I am adding the verification here https://mathoverflow.net/questions/235310/serre-mass-formula-under-extension, then both posts can be closed for me.