The long-standing goal of Artificial Intelligence (AI) has been to create human-like conversational systems. Such systems should have the ability to develop an emotional connection with the users, consequently, emotion recognition in dialogues has gained popularity. Emotion detection in dialogues is a challenging task because humans usually convey multiple emotions with varying degrees of intensities in a single utterance. Moreover, emotion in an utterance of a dialogue may be dependent on previous utterances making the task more complex. Recently, emotion recognition in low-resource languages like Hindi has been in great demand. However, most of the existing datasets for multi-label emotion and intensity detection in conversations are in English. To this end, we propose a large conversational dataset in Hindi named EmoInHindi for multi-label emotion and intensity recognition in conversations containing 1,814 dialogues with a total of 44,247 utterances. We prepare our dataset in a Wizard-of-Oz manner for mental health and legal counselling of crime victims. Each utterance of dialogue is annotated with one or more emotion categories from 16 emotion labels including neutral and their corresponding intensity. We further propose strong contextual baselines that can detect the emotion(s) and corresponding emotional intensity of an utterance given the conversational context.