Green’s Dictionary of Slang

very likely, in all likelihood.

1908		‘Doss Chiderdoss’ ‘Brief Happiness’ Sporting Times 2 May 1/3: It’s any odds on that the narrative goes / On to say that the match was ill-fated.
1936		‘Banjo’ Paterson Shearer’s Colt 69: If he can block Nancy Bell at any stage of the race it is long odds on his doing so.
1959		W. Hall Long and the Short and the Tall Act I: It’s odds on they’re just a buckshee bunch of Harries like yourselves.
1960		G.W. Target Teachers (1962) 265: First, as usual, which was odds-on anyway, being next door.
1977		G.F. Newman Villain’s Tale 59: Both lifts in the block of council flats were out of order. [...] It was odds on that the lifts in the other four flatblocks on the estate would be out of order also.
2013		T. Peacock More You Bet 7: The language of gambling and racing permeated the everyday language of the people. [...] one might have heard someone say, ‘Rain is odds-on’.