Multiple LEDs & HC-SR04
If I am understanding correctly, you have 3 LEDs ... call them A, B and C (the fact that they are a group of 14 LEDs is a red herring).  As a function of the distance measured, you want ONE of LED A, B or C lit.

Since you are using an Arduino, you have GPIO pins.  Connect a different GPIO to each of A, B and C.   You can then write an application that senses the distance (as measured by the HC-SR04) and depending on the distance returned, have a set of  "if" statements which will choose which of the GPIOs to set HIGH and the others LOW.  The GPIO set HIGH will switch on the corresponding LED.

In fact, its going to look a lot like this Instructable:

http://www.instructables.com/id/Simple-Arduino-and-HC-SR04-Example/