pr.probability – Use $ mathbb {P} ( vert hat {s} _n-s vert> x) leq a (n, x) $ y $ mathbb {P} ( vert hat {s } _n-s_n vert> x) leq b (n, x) $ to the limit $ vert s_n – s vert $

Leave $ s, s_n in mathbb {R} $ Y $ hat {s} _n $ be a random variable

I have two inequalities of concentration:

$$ mathbb {P} ( vert hat {s} _n-s vert> x) leq a (n, x) $$ for all $ n geq1 $ Y $ x> 0 $;
Y
$$ mathbb {P} ( vert hat {s} _n-s_n vert> x) leq b (n, x) $$ for all $ n geq1 $ Y $ x> 0 $.

Is there a way to tie $ vert s_n – s vert $?