In recent years, increasing attention is being paid to sentiment analysis on microblogging platforms such as Twitter. Sentiment analysis refers to the task of detecting whether a textual item (e.g., a tweet) contains an opinion about a topic. This paper proposes a probabilistic deep learning approach for sentiments analysis. The deep learning model used is a convolutional neural network (CNN). The main contribution of this approach is a new probabilistic representation of the text to be fed as input to the CNN. This representation is a matrix that stores for each word composing the message the probability that it belongs to a positive class and the probability that it belongs to a negative class. The proposed approach is evaluated on four well-known datasets HCR, OMD, STS-gold, and a dataset provided by the SemEval-2017 Workshop. The results of the experiments show that the proposed approach competes with the state-of-the-art sentiment analyzers and has the potential to detect sentiments from textual data in an effective manner.