The line is "significant" only if the coin flip results are all the same (all heads or all tails). The probability of having all the coin flips get the same result depends on the number on coins flipped (100% with one coin, 50% with two coins, 25% with three coins etc)

Easiest way is to work it out is to list the possibilities (recognizing that TTH is a different/distinct result to HTT):

HHH 9

HHT 8

HTH 8

THH 8

HTT 7

THT 7

TTH 7

TTT 6

With three coins you have 8 possible outcomes, two of which are "significant". Another way to think of it is to flip one coin, then think "what are the odds of the next two flips both being the same as the first one?" (there are four possibilities when flipping two coins, HH TH HT TT, but only one of those four will fully match your first flip, so the odds of getting three-in-a-row are once again 25%).