Nothing demanded outside ultimately diminishes chances (4)
I believe the answer is:
odds
'chances' is the definition.
(thesaurus)
'nothing demanded outside ultimately diminishes' is the wordplay.
'nothing' becomes 'o' (looks like zero - 0).
'outside' says to hollow out the word (remove centre letters).
'ultimately' indicates one should take the final letters.
'demanded' with its centre taken out is 'dd'.
The final letter of 'diminishes' is 's'.
'o'+'dd'+'s'='ODDS'
(Other definitions for odds that I've seen before include "Chances of occurrence" , "ten to one?" , "Bookies give them" , "They could be evens" , "Scraps" .)