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At first glance, exchanging Bitcoin for Monero makes sense. But why use Monero with an exchange, which is likely to help the police? (And which did.)

Monero transactions are private only on the block explorer. The sender has a key (view key) that allows one to view to whom and how much was sent.

So, what’s the point of using Monero in that case, rather than something that would resist investigators, like Zcash ?

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The sender has a key (view key) that allows one to view to whom and how much was sent.

Yes, the police have access to Shapeshift's viewkey, but they also need Wanancry's viewkey. Shapeshift's viewkey will reveal what address the Monero went to when it left Shapeshift, but where did it go next? The police will not know until they raid Wannacry's physical location and seize their viewkey. Without Wannacry's viewkey, the police can glean very little from the Monero blockchain.

You can observe the obfuscation by looking up a random transaction in a Monero blockexplorer. You will see that the receiving & change addresses are represented by one-time stealth addresses, the amount is represented by question-marks, and you can't tell which one of the 11 ring members made a monetary contribution to this (as opposed to some other) transaction.

Edit: This question has previously been answered in more detail in the Monero StackExchange site.

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