Phenomena between ill-conditioned and well-condtioned

Given that I have the following sparse matrix:

matRules = {   {1, 1} -> 0.664319, {1, 2} -> 0.335681,    {2, 2} -> 0.641645, {2, 3} -> 0.358355,    {3, 3} -> 0.584765, {3, 4} -> 0.415235,    {4, 4} -> 0.578972, {4, 5} -> 0.421028,    {5, 5} -> 0.575463, {5, 6} -> 0.424537,    {6, 6} -> 0.191367, {6, 7} -> 0.808633,    {7, 7} -> 0.704785, {7, 8} -> 0.295215,    {8, 8} -> 0.452249, {8, 9} -> 0.547751,    {9, 9} -> 0.558791, {9, 10} -> 0.441209,    {10, 10} -> 0.521902, {10, 11} -> 0.478098,    {11, 11} -> 0.441059, {11, 12} -> 0.558941,    {12, 12} -> 0.452071, {12, 13} -> 0.547929,    {13, 13} -> 0.402421, {13, 14} -> 0.597579,    {14, 1} -> 0.724525, {14, 14} -> 0.275475, {_, _} -> 0};  sparseMat = SparseArray[matRules] 

$ $ \left( \begin{array}{cccccccccccccc} 0.664319 & 0.335681 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0.641645 & 0.358355 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0.584765 & 0.415235 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0.578972 & 0.421028 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0.575463 & 0.424537 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0.191367 & 0.808633 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 0.704785 & 0.295215 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.452249 & 0.547751 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.558791 & 0.441209 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.521902 & 0.478098 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.441059 & 0.558941 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.452071 & 0.547929 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.402421 & 0.597579 \ 0.724525 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.275475 \ \end{array} \right) $ $

Then I calculate the condition number of norm-2 and norm-infinity as follows:

condInf[mat_] := LUDecomposition[mat][[-1]] cond2[mat_] := Max[#] / Min[#] &[SingularValueList[mat, Tolerance -> 0]] 

That is,

condInf@sparseMat (* 1.01157*10^8 *)  cond2@sparseMat (* 6.88491*10^7 *) 

So this matrix is ill-conditioned. However, when I remove the element {14, 1}, the matrix is well-conditioned.

matRules1 = {   {1, 1} -> 0.664319, {1, 2} -> 0.335681,    {2, 2} -> 0.641645, {2, 3} -> 0.358355,    {3, 3} -> 0.584765, {3, 4} -> 0.415235,    {4, 4} -> 0.578972, {4, 5} -> 0.421028,    {5, 5} -> 0.575463, {5, 6} -> 0.424537,    {6, 6} -> 0.191367, {6, 7} -> 0.808633,    {7, 7} -> 0.704785, {7, 8} -> 0.295215,    {8, 8} -> 0.452249, {8, 9} -> 0.547751,    {9, 9} -> 0.558791, {9, 10} -> 0.441209,    {10, 10} -> 0.521902, {10, 11} -> 0.478098,    {11, 11} -> 0.441059, {11, 12} -> 0.558941,    {12, 12} -> 0.452071, {12, 13} -> 0.547929,    {13, 13} -> 0.402421, {13, 14} -> 0.597579,    (*{14, 1} -> 0.724525,*) {14, 14} -> 0.275475, {_, _} -> 0};  sparseMat1 = SparseArray[matRules1]  condInf@sparseMat1 (* 48.8335 *)  cond2@sparseMat1 (* 35.7228 *) 

Could someone explain this phenomenon in the numerical method? Thanks a lot.