select a.value as a,b.value as b1,c11.value as c11
from table_a a
left join table_c as c11 on c11.value = 'a_1'
                        and exists(select 1 from table_b b where c11.b_pk = b.pk and b.a_pk = a.pk)
left join table_b as b on c11.b_pk = b.pk and b.a_pk = a.pk