This is not a true statement.

A:flipping a heads (on a fair coin)

B:rolling an even number (on a 6 sided normal die)

C:rolling a 5 (on a 6 sides normal die)

P(a|b)=.5=p(a) and So B favors A.

p(c|a) = 1/6 = p(c) so A favors C

p(c|b) = 0 and p(c)=1/6 and thus p(c|b)< p(c) and so we have B favors A, A favors C and C doesn't favor B