'The Tattaglia family guarantees the return of our investment'

In the film Sonny sound disbeleiving. I could never understand how this leads Sollozzo to think that he is 'hot' for the deal.

Having now read the book, that line is said in a completely different context. It tells us that Sonny says this 'eagerly'.

So now, at last, I understand - it's such an important part of the plot too!

TPM

It's not so much the fact that Sonny says it in disbelief; it's the fact that he's not agreeing with Don Corleone that makes Sollozzo initiate the hit.

Sollozzo may not have actually thought Sonny WANTED to accept his deal, but he wasn't 100% against it like Vito was, so there was a chance that with Vito out of the picture, Sonny would go along with the deal to keep some of the Corleone family's power.

It shows Sonny showed further interest in the offer, even after the Don had given his firm NO

Quite the contrary. If you remember the scene where Sollozo is holding Hagen prisoner ( for lack of a better word ) Sollozo says to Hagen " Sonny was HOT for my deal." By Sonny intervening after The Don had respectfully refused, In Sollozo's eyes it showed a "ch*nk" in the Corleone armor. Sollozo figured with Don Corleone out of the way, half the family strength would be gone and eventually Sonny would have to make the deal with him. Hagen even told Sonny, if the old man dies, you make the deal. But Sonny was to hotheaded to think that way. Sollozo F**k*d up in his judgement!


Don Cardi

The book provides a key detail: Sonny shoots his mouth off. Sollozzo's "eyes flicker, but this time with satisfaction. He had discovered a ch*nk in the Don's fortress." Sonny's indiscrete remark had given Sollozzo the idea to "divide and conquer": If he killed Vito, there'd at least be a chance that Sonny could be convinced to go along with his plan.

A little bit more from the novel to answer your question:
Michael: What made Sollozzo think he could get a deal with you?
Sonny: Sonny flushed and he didn't answer for a moment. Then he said, "We had a meeting a few months ago, Sollozzo came to us with a proposition on drugs. The old man turned him down. But during the meeting I shot off my mouth a little, I showed I wanted the deal. Which is absolutely the wrong thing to do; if there's one thing the old man hammered into me it's never to do a thing like that, to let other people know there's a split of opinion in the Family."