Get data from file using awk within strings.

i am having the text data file as below.

Processing 1
a 111111
b
c
d
e
f
Processing 2
a
b 222222
c
erorr
d
e
f
Processing 3
a
b 3333
sucessfully updated
completed data for this file ,moving to next process for this file
c
d
e
f

i want to take the line between the "processing" keyword and get the value for b in third line which will not be always constant.

o/p required.

Processing 2
a
b 222222
c
erorr
d
e
f

i have done using using sed & grep , but it has taken more amount time for it.
can you guys help me with awk ?

Please use code tags as required by forum rules!

Not sure I understand your requirement. The first value for b between "processing" lines would be empty, the next is 222222. How do you get to your "o/p required" ?