You're running into issues of Windows' compatibility between boot mode (BIOS/CSM/legacy vs. EFI/UEFI) and partition table type (MBR vs. GPT). Specifically:
/dev/sda clearly uses the old Master Boot Record (MBR) partition table type. Unless you have a third disk you're not showing, it's booting Linux in BIOS/CSM/legacy mode.
/dev/sdb clearly uses the new GUID Partition Table (GPT). To boot Windows from this disk in its current form, Windows would have to be installed in EFI/UEFI mode. Doing this might not even be possible with your current hardware (that depends on whether it's EFI-based and uses a CSM to boot Linux in BIOS/CSM/legacy mode or if it's an older BIOS-based computer). If it is possible, it would be awkward.
To step back a bit: Prior to late 2011, most computers used BIOS firmware. Computer firmware is responsible for kick-starting the boot process, and BIOS dates back to the 1980s. By today's standards, it's primitive and awkward. To replace it, EFI firmware (and its version-2.x variant, UEFI) was created. EFI is more sophisticated and flexible, but it requires new boot loaders. A final twist on this is that most EFIs for x86-64 computers include a feature, the Compatibility Support Module (CSM), which enables EFI-based computers to boot with BIOS-mode boot loaders. The CSM is awkward itself, though, and it's best to install all OSes in one mode -- that is, all in native EFI/UEFI mode or all in BIOS/CSM/legacy mode.
There are quite a few different possible ways to achieve your goal, but some of them depend on your having a newer EFI-based computer. Although I generally favor EFI-mode booting these days, I think sticking with BIOS-mode may be easier in your specific case. To do so, follow these steps:
- Use my
gdisk utility to convert
/dev/sdb from GPT to MBR form. See this page of the
gdisk documentation to learn how to do this. (Note that
gdisk is a standard part of Ubuntu.) A caveat: There is some risk to doing this conversion. It's a small risk, but it's not non-existent. You should back up your disk before attempting this conversion. If you don't have the means to back up your disk, acquire it; disk failures, user errors, bugs, and other problems wipe out data all the time, even when you don't take risks with GPT-to-MBR conversions and the like.
- If desired or necessary, use GParted to create additional partitions on
/dev/sdb. Do not let the Windows installer create partitions! On MBR disks, the Windows partitioning tools are a nightmare, and can create a configuration that's next to useless under Ubuntu. If you want to stick with the two-partition setup you've got now (but converted to MBR form), you should be fine, so long as the Windows installer doesn't try to create lots more partitions. (Problems really begin when Windows tries to create a configuration with more than four partitions on an MBR disk.)
- Launch the Windows installer and install to the Windows partition you've created on
- There's a chance that Windows will take over the boot process. In this case, you'll need to run Boot Repair from an Ubuntu emergency disk. I'd be ready with an Ubuntu installation/emergency disk just in case this becomes necessary.
- If necessary, boot into Ubuntu and run
sudo update-grub. This will tell Ubuntu to reconfigure GRUB so that it detects Windows and offers an option to boot Windows on GRUB's menu.
The other major approach is to convert Ubuntu to boot in EFI mode and install Windows in that mode, too. Clearly, though, you're booting the Windows installer in BIOS mode (that's why it's complaining about the disk being GPT; Windows won't install to or boot from a GPT disk when booted in BIOS mode), so it's uncertain that you've even got an EFI-based computer; and if you do, you'll need to find a way to boot your installer in EFI mode rather than in BIOS mode. If you go with this approach, you'll definitely need to install a new EFI-mode Linux boot loader after you've installed Windows. Boot Repair can do this, but you'll need to boot the Ubuntu emergency disk in EFI mode.
As background reading, particularly if you think you've got an EFI-based computer, and especially if you try to go the EFI route, I recommend you read my page on the CSM. This page is written for people in a different situation from yours, but it describes what the CSM is and how it can complicate the boot process. My recommendation to install Windows in BIOS/CSM/legacy mode is at odds with the general theme of my CSM page, but given that your existing Ubuntu installation is almost certainly in BIOS/CSM/legacy mode and you're clearly booting the Windows installer in that same mode, it seems that sticking with that mode is the course of least resistance, even though that will require changing
/dev/sdb from GPT to MBR.