I am planning to send my proposal to potential supervisor before formally applying, however there are 3 different professors who have the exact same research interests in their profile and all of them would be perfect for my proposed topic. I do not want to send it to the school for them the forward it to a random teacher for initial opinion. Would it be rude if I send it to more than one potential supervisors, what if they find out?

It seems a bit strange they all have the exact same research interests and are at the same institution... Do they all publish work together or something? Are you sure one is not the PI and the others are PhD students/postdocs etc?

In any case, they will definitely talk to each other and I would advise against applying to them all. PIs with similar research interests at different institutions know each other and I know they talk about which students have contacted them with proposals. They may think you are not particularly interested in them and just want any PI/project if you apply to them all.

Are you applying through findaphd.com or just randomly contacting them?