Step 1 :Calculate the total number of tickets in the box: \(13 \times 100 + 15 \times 50 + 13 \times 25 + 20 = 1300 + 750 + 325 + 20 = 2395\) tickets.
Step 2 :Identify the number of 'dummy' tickets: 20 tickets.
Step 3 :Calculate the probability of drawing the first 'dummy' ticket: \(\frac{20}{2395}\).
Step 4 :Calculate the probability of drawing the second 'dummy' ticket, after one has already been drawn: \(\frac{19}{2394}\).
Step 5 :Calculate the probability of drawing the third 'dummy' ticket, after two have already been drawn: \(\frac{18}{2393}\).
Step 6 :Calculate the total probability that all three tickets drawn have no money value: \(\frac{20}{2395} \times \frac{19}{2394} \times \frac{18}{2393}\).
Step 7 :\(\boxed{0.000056}\) is the probability that all three tickets drawn have no money value, or 0.0056% when expressed as a percentage.