Meta-learning aims to learn a model that can handle multiple tasks generated from an unknown but shared distribution. However, typical meta-learning algorithms have assumed the tasks to be similar such that a single meta-learner is sufficient to aggregate the variations in all aspects. In addition, there has been less consideration of uncertainty when limited information is given as context. In this paper, we devise a novel meta-learning framework, called Meta-learning Amidst Heterogeneity and Ambiguity (MAHA), that outperforms previous works in prediction based on its ability to task identification. By extensively conducting several experiments in regression and classification, we demonstrate the validity of our model, which turns out to generalize to both task heterogeneity and ambiguity.