Like one imprisoned in Eastern city? Without a doubt (6)

I believe the answer is:
easily
'without a doubt' is the definition.
I can't tell whether this definition defines the answer.
'like one imprisoned in eastern city?' is the wordplay.
'like' becomes 'as'.
'one' becomes 'i' (Roman numeral).
'imprisoned in' is an insertion indicator.
'eastern city?' becomes 'ely' (Ely is a city in Cambridgeshire. I am not sure about the 'eastern' bit.).
'as'+'i'='asi'
'asi' put inside 'ely' is 'EASILY'.
Can you help me to learn more?
(Other definitions for easily that I've seen before include "without a hitch?" , "Without difficulty or effort" , "Simply" , "no problem!" , "Effortlessly" .)
