The sample space for all 3 problems contains 26 equally 
likely choices:

{a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}

1. vowel

Set of successful letters contains 5 equally likely choices
from the sample space:  {a,e,i,o,u}

That's 5 out of 26 or a probability of 5/26

2. precedes m and is a vowel

Set of successful letters contains 3 equally likely choices
from the sample space:  {a,e,i}

That's 3 out of 26 or a probability of 3/26.

2. succeeds n and is a vowel

Set of successful letters contains 2 equally likely choices
from the sample space:  {o,u}

That's 2 out of 26 or a probability of 2/26, which reduces 
to 1/13.

Edwin