This does already exist and is called "Smart Contracts" in Etherium. It's a blockchain-based "world computer" as they call it themselves. What you would do is code up a smart contract that contains the requirements that you need and have it hold funds (in the case of a bet or something). The contract itself would own the funds and none of the participants in the contract would have the option of removing them from there unless under the conditions that are specifically programmed into the contract.

The issue that you mostly have with this is that the Etherium program (the contract) can not have any contact with the outside world. It cannot look at a sports or weather website to see who should get paid. You need some other way of giving the payout triggers to the contract. One way would be to use one or more trusted services to post the weather or sports results to the Etherium blockchain (in another contract). Your contract can then use that other contract's data to decide who needs to get paid.

Another issue is that the contract cannot trigger itself. It cannot decide that it needs to pay Alice or Bob and then do that. Once the results are in (the sports results are known in the blockchain), someone - probably the winner - will have to ask the contract to process the results and pay out.

In short: A Smart Contract doesn't have to be trusted by anyone, the contract itself is in control of the money involved and not any of the participants or even a trusted third party.

As for the legal status of a smart contract, good question. You'd have to make sure that the initial creating of the contract by both parties is also in the blockchain. You cannot just upload a contract with Alice and Bob's addresses hardcoded in there. You have to make sure that the deployment of the contract and the agreement of both parties to the terms of the contract is explicitly recorded in the blockchain. Alice and Bob will have to both make a transaction to the contract, depositing their funds and signaling their willingness to participate.