Is there a way to add onto previous lines in my display without printing new lines?

I am making a horse race program and I have to display something like

Horse 1: 0

Horse 2: 0

Horse 3: 0

The horse "positions" are in an array and I will be using a ran num generator to generate a number from 1-3 and then that will be added to the previous positions to simulate the horses moving. Is there a way to make it so that the display updates the new positions rather than printing all of the positions again? This is an example of the code that I simplified to show how it prints twice. Also, is there a way to loop the adding until one of the horses wins at 15? Would I use a while statement? Thank you in advance.

import java.util.*;
public class ArrayRandom{
  public static void main(String[ ] args){
   final int SIZE = 3;
   Random ran = new Random( ); 
   int[ ] arrRan = new int[SIZE];
   //populating the array one number at the time
  for(int i = 0; i<arrRan.length; i++){
     arrRan[i] = ran.nextInt(3) + 1; 
}
System.out.println("The horse positions are:");
System.out.println("Horse 1: " + arrRan[0]);
System.out.println("Horse 2: " + arrRan[1]);
System.out.println("Horse 3: " + arrRan[2]);

for(int i = 0; i<arrRan.length; i++){
  arrRan[i] = arrRan[i] + (ran.nextInt(3) + 1); 
}
System.out.println("The horse positions are:");
System.out.println("Horse 1: " + arrRan[0]);
System.out.println("Horse 2: " + arrRan[1]);
System.out.println("Horse 3: " + arrRan[2]);

for(int i = 0; i<arrRan.length; i++){
  arrRan[i] = arrRan[i] + (ran.nextInt(3) + 1); 
}
System.out.println("The horse positions are:");
System.out.println("Horse 1: " + arrRan[0]);
System.out.println("Horse 2: " + arrRan[1]);
System.out.println("Horse 3: " + arrRan[2]);
 }
}