"The context in John 17:3 is specifically separating out those who know Him, meaning will not just have eternal life, but eternal life with HIM. Big difference. But to KNOW Him, we accept the conviction of the Holy Spirit working in this world to convict all men of their sins. Those that believe will have that kind of eternal life, life with HIM." (italics mine)
Im not sure I get exactly what you mean. What is the other type of eternal life you are talking about?