Before revision:  Especially we show that a probability of a tropical line segment of randomly chosen two trees going thorough the origin (the star tree) is zero and we also show that if two given trees differ only one nearest neighbor interchange (NNI) move, then the tree topology of a tree in the tropical line segment between them is the same tree topology of one of these given two trees with possible zero branch lengths.
After revision:  Especially we show that a probability of a tropical line segment of two randomly chosen trees going thorough the origin (the star tree) is zero and we also show that if two given trees differ only one nearest neighbor interchange (NNI) move, then the tree topology of a tree in the tropical line segment between them is the same tree topology of one of these given two trees with possible zero branch lengths.