If we have an electron in a one-dimensional infinite potential well, and we have measured its position and found it to be let's say at $x=0$ at the center of the well. The state vector after measurement becomes $|x=0>.$ If we calculate the probability then to get any eigen-value of the energy we will find it to be $1/a$ where $a$ is the width of the well. But that means the total probability (the sum of infinite terms each equals $1/a$) is infinite which is absurd. So, what exactly is happening here please?
When the distribution of probabilities is continuous, the probability of finding an object exactly at one specific position is zero. You can calculate what is the probability of finding the object at a certain interval, you have a probability density. The right way to treat the probability is $dP(x)=dx/a$, and the total probability now becomes 1, because $\int dP(x)=\int^a_0 dx/a=1$. For more details see https://en.wikipedia.org/wiki/Particle_in_a_box