Put the original piece of wire onto the number line, from 0 to 6. Let x be the coordinate, where you cut. Then the condition that both cuts will be at least 1 in long, is this inequality 1 < x < 5. So, the cutting position "x" must lie in the segment [1,5] of the entire piece of the length 6. Hence, the probability under the question is= = 66.66%.