Etiquette, manners and questions related to private and personal conversation and communication
People not involving third person in their conversation, is it allowed?
Islamic Answers and Ruling:
Al-Bukhaari (6290) and Muslim (2184) narrated that ‘Abdullah ibn Mas‘ood (may Allah be pleased with him) said: The Prophet (blessings and peace of Allah be upon him) said: “If you are three, two should not converse privately to the exclusion of the other one until you join some other people, so that you do not make him sad.”
At-Tirmidhi (2825) narrated that ‘Abdullah ibn Mas‘ood said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “If you are three, two should not converse privately to the exclusion of their companion.” Classed as saheeh by Shaykh al-Albaani in Saheeh Sunan at-Tirmidhi.
There are some cases in which an exception is made from the prohibition on conversing privately that is mentioned in the hadiths:
1.. The first case is when two converse privately with the permission of the third; so if he gives them permission, it is permissible, because of the reports narrated by Ahmad (6302) from Ibn ‘Umar (may Allah be pleased with him), who said:
The Messenger of Allah (blessings and peace of Allah be upon him) said: “If you are three, two should not converse privately to the exclusion of the third, except with his permission, for that will make him sad.”
2.. The second case is when the number is more than three, in which case it is permissible for two to converse privately to the exclusion of the others, because of the report narrated by Abu Dawood (4581), in which it says: Abu Saalih said: I said to Ibn ‘Umar: (What if they are) four? He said: Then it does not matter.
3.The third case is when there is a need or interest that outweighs any negative consequences of the private conversation. In that case, it is permissible for two to converse to the exclusion of the third.
Refer complete answer
https://islamqa.info/en/answers/183568/rulings-and-issues-having-to-do-with-private-conversations