Sketches can be categorized as personal, shared, persuasive, and handover sketches. Depending on each category, their level of ambiguity also varies. The applications of sketches includes conceptual design, eliciting user preferences, shape retrieval, and sketch-based modeling. There is a need for quantification of uncertainty in sketches in mapping of sketches to 3D models in sketch-based modeling, in eliciting user preferences, and in tuning the level of uncertainty in sketches at the conceptual design stage. This paper investigates the role of probability of importance in quantifying the level of uncertainty in sketches by raising the following three research questions: How are the features in a sketch ranked? What is the probability of importance of features in a sketch? What is the level of uncertainty in a sketch? This paper presents an improved framework for uncertainty quantification in sketches. The framework is capable of identifying and ranking the features in the sketch, determining their probability of importance, and finally quantifying the level of uncertainty in the sketch. Ranking the features of a sketch is performed by a hierarchical approach, whereas probability of importance is determined by assessing the probability of likeliness using a shape matching approach and a probability transformation. Quantification of uncertainty is accomplished by using the principle of normalization of entropy. A case study of a bicycle sketch is used to demonstrate that the framework eliminates the need of expert input in assessment of uncertainty in sketches, and, hence, can be used by design practitioners with limited experience.