Internet-related personal communication has increased significantly in the course of recent years. Simultaneously, the possibility of sharing sensitive personal information has become a part of everyday life. Thus, the possibility of privacy violations and leaking of personal data has arisen. This paper analyzes the extent to which Internet users trust that the privacy of their private messages is protected and upheld in web-based messaging services such as Facebook Messenger and WhatsApp. The paper examines how users' trust in other people (social trust) and trust in institutional actors (such as the parliamentary system and police) predict a high probability to trust that their private and confidential messages are not disclosed. The analysis is conducted based on data (n=1648) that was gathered through a nationwide survey in Finland. Results show that both high social trust and institutional trust are associated with high trust in the confidentiality and privacy of messages that are sent through messaging services on the web. Demographic factors did not have a remarkable effect on how trusting users are. Finally, a decomposition analysis shows that social trust is the strongest predictor even when institutional trust and demographic factors are controlled for.