Hi!
It solely depends on the topic of the conversation. If it is something personal (such as feelings for someone or family matters), it means that they are opening up to you—sharing what they are going through. It is not your place to expose or tell anyone what they told you. Them expressing what they feel and displaying their emotions in private indicates that they trust you very much. If you, instead of supporting them and providing a helping hand, go and talk to someone about what they expressed to you, it is certainly an invasion of privacy because you are not respecting their sentiments.
Although, as I said, it entirely depends on the circumstances. If someone talks to you in private about anything that may cause harm to them or is hurting their well-being, it certainly is not wrongful from your side to consult someone about the difficulty they (the person who confided their personal feelings to you) are facing because sometimes you are not capable of helping them. Thus, it is essential to recognize the situation. If it is the second case, try finding someone trustworthy to support the particular person and help them through their difficulties. In this case, even though you are talking to someone about a private conversation you had with the person going through a tough time, it is not an invasion of privacy because you are helping the person seek help and support you cannot necessarily provide.
Hope this helps!
Thanks,
Dear Letterbox