Sarcasm, sentiment, and emotion are three typical kinds of spontaneous affective responses of humans to external events and they are tightly intertwined with each other. Such events may be expressed in multiple modalities (e.g., linguistic, visual and acoustic), e.g., multi-modal conversations. Joint analysis of humans' multi-modal sarcasm, sentiment, and emotion is an important yet challenging topic, as it is a complex cognitive process involving both cross-modality interaction and cross-affection correlation. From the probability theory perspective, cross-affection correlation also means that the judgments on sarcasm, sentiment, and emotion are incompatible. However, this exposed phenomenon cannot be sufficiently modelled by classical probability theory due to its assumption of compatibility. Neither do the existing approaches take it into consideration. In view of the recent success of quantum probability (QP) in modeling human cognition, particularly contextual incompatible decision making, we take the first step towards introducing QP into joint multi-modal sarcasm, sentiment, and emotion analysis. Specifically, we propose a QUantum probabIlity driven multi-modal sarcasm, sEntiment and emoTion analysis framework, termed QUIET. Extensive experiments on two datasets and the results show that the effectiveness and advantages of QUIET in comparison with a wide range of the state-of-the-art baselines. We also show the great potential of QP in multi-affect analysis.