How to obtain likelihood ($P(B/R)$ given the prior $P(R)$ and the posterior $P(R/B)$

Question

I am working on a topic related to multiple-choice response. I would like to measure the efficiency of the information source (or a student’s information search) and I believe Bayesian statistics is the right approach; however, since I only know the basics, I would like to present it to see if my reasoning is coherent or not. Given a multiple-choice question (e.g., with 4 answers) where only one answer is correct, a student can answer it solely based on what he/she studied at home, assigning a probability to each answer, for example, P(R)=(0.4, 0.3, 0.15, 0.15). The response might end there, or the student might consult a book and update those probabilities, for example, P(R|B)=(0.4,0.6,0,0). P(R) would be the prior probability, P(R|B) would be the posterior probability, both (multinomial) and P(B/R) would be the likelihood, which I understand to be the update of my prior belief P(R) and convert it in P(R|B). So I want to know P(B|R) and I would also like to see if I can determine what P(B|R) would make P(R|B)=(1,0,0,0), that is, make the correct answer chosen with certainty. I understand that this is a kind of inverse problem, which will not have a unique solution; but perhaps there is some heuristic to approximate a solution, at least for the first challenge of finding P(B|R). Thank you for your help!