$1-\sum_{x=0}^{13} b(x ; 19,0.7)$

Step 1 ：The problem is asking for the value of \(1-\sum_{x=0}^{13} b(x ; 19,0.7)\), where \(b(x ; 19,0.7)\) is the binomial probability function.

Step 2 ：The binomial probability function is defined as \(b(x ; n, p) = \binom{n}{x} p^x (1-p)^{n-x}\), where \(\binom{n}{x}\) is the binomial coefficient, \(p\) is the probability of success, \(n\) is the number of trials, and \(x\) is the number of successes.

Step 3 ：In this case, \(n=19\), \(p=0.7\), and we are summing over all \(x\) from 0 to 13.

Step 4 ：The sum of the binomial probabilities for \(x\) from 0 to 13 is calculated to be approximately 0.5261374757264861.

Step 5 ：Subtracting this sum from 1 gives the final answer of approximately 0.47386252427351394.

Step 6 ：Final Answer: \(\boxed{0.47386252427351394}\)