Open book examination is useful when the information that is being asked in the exam is very extensive and it is not important to remember them. Open book examination can improve your reference skills and the information you actually remember is where you can find certain information in the reference books. So you can see that open book exams are good for professions that need reference material.
Many professions need a lot of reference material. For example law. In this subject you need to understand and memorize the different laws of the land. There are so many that you have to specialize in civil, criminal, cyber etc. Each day there is a ruling coming out of the court that can become a benchmark or reference point for a case that some lawyer is handling. In the years as a student each lawyer has to go through many rulings and cases to familiarize himself with the nuances of court rulings. So while remembering and understanding various laws should be a closed book exam, the court ruling reference material can be an open book exam. This same scenario can be applied to medicine and engineering.