Ranking System on Multiple Choice Tests

Suppose we have a Multiple Choice Test with the following characteristics:

• There are M available multiple choice Questions on the system
• There are N users participating
• Each user replies to K questions, for convenience let's assume K < M
• Eventually, we can define the difficulty level of each question by computing the population's probability of answering correctly eg

I believe you should sum the inverses of $P_{i \mathrm{correct}}$. So the score of each player will be: score $\sum_{i=0}^N \left(\cfrac{1}{P_{i \mathrm{correct}}}\right)$ for $i = 1..N$