Ordering Three Geometric Waits

Lewis, Scout and Rupert each flip their own fair coin until the first heads. $L$, $S$ and $R$ are the number of flips each needs, iid Geometric(1/2) on ${1, 2, 3, \dots}$.

total = 0.0
for l in range(1, 400):
    for s in range(l, 400):
        total += 0.5**l * 0.5**s * 0.5**(s - 1)   # P(L=l) * P(S=s) * P(R>=s)
print(round(total, 3))

What does this print, that is, what is $P(L \leq S \leq R)$?

Answer format: round to 3 decimal places.