From January 2021 I have been working on the project "Verified Probabilistic Verification". There are a multitude of ways to verify whether systems or software work as intended. One such way is Model Checking. My interest lies in Probabilistic Model Checking which is capable of verifying systems that have random behavior. However, one of the core algorithms for this type of model checking, called value iteration, has been proven to be faulty. To restore the faith in our tools, I want to prove the correctness of these algorithms in the theorem prover "Isabelle/HOL". I use the Isabelle Refinement Framework to generate a fast correct-by-construction code that can be used to validate other model checkers and that can even be fast enough to be embedded in existing model checkers such as the Modest Toolset.