Lalit has the most practical answer. However, you wanted the resulting grey to be the average of the red, green and blue and should set up your matrix like so:
float oneThird = 1/3f;
float[] mat = new float[]{
oneThird, oneThird, oneThird, 0, 0,
oneThird, oneThird, oneThird, 0, 0,
oneThird, oneThird, oneThird, 0, 0,
0, 0, 0, 1, 0,};
ColorMatrixColorFilter filter = new ColorMatrixColorFilter(mat);
paint.setColorFilter(filter);
c.drawBitmap(original, 0, 0, paint);
And finally, as I have faced the problem of converting an image to grayscale before - the most visually pleasing result in all cases is achieved by not taking the average, but through giving each colour different weight depending on its percieved brightness, I tend to use these values:
float[] mat = new float[]{
0.3f, 0.59f, 0.11f, 0, 0,
0.3f, 0.59f, 0.11f, 0, 0,
0.3f, 0.59f, 0.11f, 0, 0,
0, 0, 0, 1, 0,};